Изменения

Таблица умножения(таблица Кэли) — таблица, которая описывает структуру конечных алгебраических систем с одной бинарной операцией. Таблица позволяет определить, является ли группа абелевой, найти ядро группы и обратные элементы по отношению к другим элементам в этой группе.

 '''=== Структура'''===Пусть <mathtex>\mathbb{A}_n</math> = <math>\{a_1,a_2,\dots,a_n\}</mathtex> - — группа из <tex>n </tex> элементов.

|statement=Каждая строка или столбец являются перестановкой элементов группы.|proof=Пусть <tex>a,b,c,d \in G</tex>. Тогда <tex>a*bab=d \enskip \& \enskip a*c</tex> и <tex>ac=d \Rightarrow b=c</tex>. Так как количество клеток в строке равно количеству элементов, то, по принципу Дирихле, каждый элемент группы встречается в строке один раз.

|statement=Если таблица симметрична относительно главной диагонали, то операция умножения коммутативна.|proof=Таблица симметрична <tex>\Rightarrow a*b ab = b*aba</tex> для любых <tex>a,b \in G</tex>

|statement=Все В конечной группе порядок каждого элемента является делителем порядка группы простого порядка <tex>p</tex> изоморфны <tex>\mathbb{Z}/p\mathbb{Z}</tex>.

|statement=В простой группе порядок каждого элемента является делителем Все группы простого порядка группы<tex>p</tex> изоморфны <tex>\mathbb{Z}/p\mathbb{Z}</tex>.

1) n Ниже перечислены все группы до шестого порядка включительно: * <tex>|G| = 1</tex>Тривиальная группа

* <tex>|G| = 2) n = </tex>Группа вычетов по модулю два относительно сложения: <tex>\mathbb{Z}/2\mathbb{Z}</tex>

!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big> !style="background:#efefef;"| <big>a1</big>

!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big>

!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>e0</big>

* <tex>|G| = 3) n = </tex>Группа вычетов по модулю три относительно сложения: <tex>\mathbb{Z}/3\mathbb{Z}</tex>

!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big> !style="background:#efefef;"| <big>a1</big> !style="background:#efefef;"| <big>b2</big>

!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big> || <big>b2</big>

!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>b2</big> || <big>e0</big>

!style="background:#efefef;"| <big>b2</big>| <big>b2</big> || <big>e0</big> || <big>a1</big>

* <tex>|G| = 4) n = </tex>Группа вычетов по модулю четыре относительно сложения: <tex>\mathbb{Z}/4\mathbb{Z}</tex>

!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big> !style="background:#efefef;"| <big>a1</big> !style="background:#efefef;"| <big>b2</big> !style="background:#efefef;"| <big>c3</big>

!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big> || <big>b2</big> || <big>c3</big>

!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>e0</big> || <big>c3</big> || <big>b2</big>

!style="background:#efefef;"| <big>b2</big>| <big>b2</big> || <big>c3</big> || <big>e0</big> || <big>a1</big>

!style="background:#efefef;"| <big>c3</big>| <big>c3</big> || <big>b2</big> || <big>a1</big> || <big>e0</big>

!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e(0,0)</big> !style="background:#efefef;"| <big>a(0,1)</big> !style="background:#efefef;"| <big>b(1,0)</big> !style="background:#efefef;"| <big>c(1,1)</big>

!style="background:#efefef;"| <big>e(0,0)</big>| <big>e(0,0)</big> || <big>a(0,1)</big> || <big>b(1,0)</big> || <big>c(1,1)</big>

!style="background:#efefef;"| <big>a(0,1)</big>| <big>a(0,1)</big> || <big>b(0,0)</big> || <big>c(1,1)</big> || <big>e(1,0)</big>

!style="background:#efefef;"| <big>b(1,0)</big>| <big>b(1,0)</big> || <big>c(1,1)</big> || <big>e(0,0)</big> || <big>a(0,1)</big>

!style="background:#efefef;"| <big>c(1,1)</big>| <big>c(1,1)</big> || <big>e(1,0)</big> || <big>a(0,1)</big> || <big>b(0,0)</big>

!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big> !style="background:#efefef;"| <big>a1</big> !style="background:#efefef;"| <big>b2</big> !style="background:#efefef;"| <big>c</big> |-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b3</big> || <big>c</big>|-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big>|-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>e</big>|-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>e</big> || <big>a</big>|}5) n = 5{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big> !style="background:#efefef;"| <big>a</big> !style="background:#efefef;"| <big>b</big> !style="background:#efefef;"| <big>c</big> !style="background:#efefef;"| <big>d</big>

!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big> || <big>b2</big> || <big>c3</big> || <big>d4</big>

!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>b2</big> || <big>c3</big> || <big>d4</big> || <big>e0</big>

!style="background:#efefef;"| <big>b2</big>| <big>b2</big> || <big>c3</big> || <big>d4</big> || <big>e0</big> || <big>a1</big>

!style="background:#efefef;"| <big>c3</big>| <big>c3</big> || <big>d4</big> || <big>e0</big> || <big>a1</big> || <big>b2</big>

!style="background:#efefef;"| <big>d4</big>| <big>d4</big> || <big>e0</big> || <big>a1</big> || <big>b2</big> || <big>c3</big>

* <tex>|G| = 6) n = </tex>Группа вычетов по модулю шесть относительно сложения: <tex>\mathbb{Z}/6\mathbb{Z}</tex>

!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big>!style="background:#efefef;"| <big>a1</big>!style="background:#efefef;"| <big>b2</big>!style="background:#efefef;"| <big>c3</big>!style="background:#efefef;"| <big>d4</big>!style="background:#efefef;"| <big>f5</big>

!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big> || <big>b2</big> || <big>c3</big> || <big>d4</big> || <big>f5</big>

!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>e2</big> || <big>c3</big> || <big>b4</big> || <big>f5</big> || <big>d0</big>

!style="background:#efefef;"| <big>b2</big>| <big>b2</big> || <big>c3</big> || <big>d4</big> || <big>f5</big> || <big>e0</big> || <big>a1</big>

!style="background:#efefef;"| <big>c3</big>| <big>c3</big> || <big>b4</big> || <big>f5</big> || <big>d0</big> || <big>a1</big> || <big>e2</big>

!style="background:#efefef;"| <big>d4</big>| <big>d4</big> || <big>f5</big> || <big>e0</big> || <big>a1</big> || <big>b2</big> || <big>c3</big>

!style="background:#efefef;"| <big>f5</big>| <big>f5</big> || <big>d0</big> || <big>a1</big> || <big>e2</big> || <big>c3</big> || <big>b4</big>

| <big>e</big> || <big>a</big> || <big>baa</big> || <big>cb</big> || <big>dc</big> || <big>fd</big>

| <big>a</big> || <big>eaa</big> || <big>ce</big> || <big>dc</big> || <big>fd</big> || <big>b</big>

!style="background:#efefef;"| <big>baa</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>faa</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>cd</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>dc</big>

!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>faa</big> || <big>a</big> || <big>e</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>f</big> || <big>b</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big>

| <big>c</big> || <big>b</big> || <big>d</big> || <big>ea</big> || <big>fe</big> || <big>aaa</big>

| <big>d</big> || <big>f</big> || <big>ac</big> || <big>b</big> || <big>eaa</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>da</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b</big>

{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>e</big> || <big>b</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>bДля группы </bigtex> |} \mathbb{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |S} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e_3</bigtex>!style="background:#efefef;"| <bigtex>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</bigtex>!style="background:#efefef;"| — это циклическая перестановка <bigtex>d(123)\rightarrow(231)</bigtex>!style="background:#efefef;"| , а <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <bigtex>b</big> || <big>,\,c</big> || <big>,\,d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</bigtex> || — транспозиции <bigtex>e(123)\rightarrow(213),\,(123)\rightarrow(132),\,(123)\rightarrow(321)</bigtex> || <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>b</big> || <big>e</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>b</big> || <big>a</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>e</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>b</big> || <big>a</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>b</big> || <big>a</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} соответственно.