Conjugacy class search results

Results (22 matches)

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Elements of the group are displayed as permutations of degree 8.

Group	Label	Order	Size	Centralizer	Powers				Representative
					2P	3P	5P	7P
$S_8$	1A	$1$	$1$	$S_8$	1A	1A	1A	1A	$()$
$S_8$	2A	$2$	$28$	$C_2\times S_6$	1A	2A	2A	2A	$(7,8)$
$S_8$	2B	$2$	$105$	$C_2\wr S_4$	1A	2B	2B	2B	$(1,6)(2,4)(3,7)(5,8)$
$S_8$	2C	$2$	$210$	$D_4\times S_4$	1A	2C	2C	2C	$(2,3)(5,8)$
$S_8$	2D	$2$	$420$	$C_2^2\times S_4$	1A	2D	2D	2D	$(2,4)(3,7)(5,6)$
$S_8$	3A	$3$	$112$	$C_3\times S_5$	3A	1A	3A	3A	$(3,5,4)$
$S_8$	3B	$3$	$1120$	$C_6\times S_3$	3B	1A	3B	3B	$(1,8,2)(4,6,5)$
$S_8$	4A	$4$	$420$	$C_4\times S_4$	2C	4A	4A	4A	$(2,5,3,8)$
$S_8$	4B	$4$	$1260$	$C_4\wr C_2$	2B	4B	4B	4B	$(1,8,6,7)(2,5,4,3)$
$S_8$	4C	$4$	$1260$	$C_4\times D_4$	2C	4C	4C	4C	$(1,2)(3,4,7,8)(5,6)$
$S_8$	4D	$4$	$2520$	$C_2^2\times C_4$	2C	4D	4D	4D	$(1,6,4,3)(2,5)$
$S_8$	5A	$5$	$1344$	$C_5\times S_3$	5A	5A	1A	5A	$(2,4,5,7,8)$
$S_8$	6A	$6$	$1120$	$C_6\times S_3$	3A	2A	6A	6A	$(3,4,5)(7,8)$
$S_8$	6B	$6$	$1120$	$C_6\times S_3$	3B	2A	6B	6B	$(1,2)(3,4,7)(5,6,8)$
$S_8$	6C	$6$	$1680$	$C_3\times D_4$	3A	2C	6C	6C	$(1,7,4)(2,3)(5,8)$
$S_8$	6D	$6$	$3360$	$C_2\times C_6$	3B	2B	6D	6D	$(1,4,8,6,2,5)(3,7)$
$S_8$	6E	$6$	$3360$	$C_2\times C_6$	3B	2D	6E	6E	$(2,7,6,4,3,5)$
$S_8$	7A	$7$	$5760$	$C_7$	7A	7A	7A	1A	$(1,5,6,4,2,8,3)$
$S_8$	8A	$8$	$5040$	$C_8$	4B	8A	8A	8A	$(1,2,8,5,6,4,7,3)$
$S_8$	10A	$10$	$4032$	$C_{10}$	5A	10A	2A	10A	$(2,7,3,6,4)(5,8)$
$S_8$	12A	$12$	$3360$	$C_{12}$	6C	4A	12A	12A	$(1,4,7)(2,8,3,5)$
$S_8$	15A	$15$	$2688$	$C_{15}$	15A	5A	3A	15A	$(1,3,6)(2,5,8,4,7)$

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