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Results (45 matches)

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Elements of the group are displayed as permutations of degree 10.

Group Label Order Size Centralizer Powers Representative
2P 3P
$S_4\times S_3^2$ 1A $1$ $1$ $S_4\times S_3^2$ 1A 1A $()$
$S_4\times S_3^2$ 2A $2$ $3$ $D_6\times S_4$ 1A 2A $(1,5)(2,4)(3,6)$
$S_4\times S_3^2$ 2B $2$ $3$ $D_6\times S_4$ 1A 2B $(1,6)(2,4)(3,5)$
$S_4\times S_3^2$ 2C $2$ $3$ $D_4\times S_3^2$ 1A 2C $(7,9)(8,10)$
$S_4\times S_3^2$ 2D $2$ $6$ $D_6^2$ 1A 2D $(9,10)$
$S_4\times S_3^2$ 2E $2$ $9$ $D_4\times D_6$ 1A 2E $(1,5)(2,4)(3,6)(7,8)(9,10)$
$S_4\times S_3^2$ 2F $2$ $9$ $D_4\times D_6$ 1A 2F $(1,6)(2,4)(3,5)(7,8)(9,10)$
$S_4\times S_3^2$ 2G $2$ $9$ $C_2^2\times S_4$ 1A 2G $(3,4)(5,6)$
$S_4\times S_3^2$ 2H $2$ $18$ $C_2^2\times D_6$ 1A 2H $(1,6)(2,4)(3,5)(7,9)$
$S_4\times S_3^2$ 2I $2$ $18$ $C_2^2\times D_6$ 1A 2I $(1,5)(2,4)(3,6)(7,10)$
$S_4\times S_3^2$ 2J $2$ $27$ $C_2^2\times D_4$ 1A 2J $(3,4)(5,6)(7,8)(9,10)$
$S_4\times S_3^2$ 2K $2$ $54$ $C_2^4$ 1A 2K $(2,5)(3,4)(7,9)$
$S_4\times S_3^2$ 3A $3$ $2$ $C_6^2:D_6$ 3A 1A $(1,3,4)(2,5,6)$
$S_4\times S_3^2$ 3B $3$ $2$ $C_6^2:D_6$ 3B 1A $(1,3,4)(2,6,5)$
$S_4\times S_3^2$ 3C $3$ $4$ $C_3^2\times S_4$ 3C 1A $(2,6,5)$
$S_4\times S_3^2$ 3D $3$ $8$ $C_3\times S_3^2$ 3D 1A $(8,10,9)$
$S_4\times S_3^2$ 3E $3$ $16$ $S_3\times C_3^2$ 3E 1A $(1,3,4)(2,5,6)(7,10,9)$
$S_4\times S_3^2$ 3F $3$ $16$ $S_3\times C_3^2$ 3F 1A $(1,4,3)(2,5,6)(7,10,9)$
$S_4\times S_3^2$ 3G $3$ $32$ $C_3^3$ 3G 1A $(1,3,4)(7,9,10)$
$S_4\times S_3^2$ 4A $4$ $6$ $C_4\times S_3^2$ 2C 4A $(7,10,9,8)$
$S_4\times S_3^2$ 4B $4$ $18$ $C_4\times D_6$ 2C 4B $(1,6)(2,4)(3,5)(7,10,9,8)$
$S_4\times S_3^2$ 4C $4$ $18$ $C_4\times D_6$ 2C 4C $(1,5)(2,4)(3,6)(7,9,8,10)$
$S_4\times S_3^2$ 4D $4$ $54$ $C_2^2\times C_4$ 2C 4D $(2,5)(3,4)(7,8,10,9)$
$S_4\times S_3^2$ 6A $6$ $6$ $C_6\times S_4$ 3A 2A $(1,2,3,5,4,6)$
$S_4\times S_3^2$ 6B $6$ $6$ $C_6\times S_4$ 3B 2B $(1,2,3,6,4,5)$
$S_4\times S_3^2$ 6C $6$ $6$ $C_{12}:D_6$ 3A 2C $(1,4,3)(2,6,5)(7,9)(8,10)$
$S_4\times S_3^2$ 6D $6$ $6$ $C_{12}:D_6$ 3B 2C $(1,4,3)(2,5,6)(7,9)(8,10)$
$S_4\times S_3^2$ 6E $6$ $12$ $C_6\times D_6$ 3A 2D $(1,3,4)(2,5,6)(9,10)$
$S_4\times S_3^2$ 6F $6$ $12$ $C_6\times D_6$ 3B 2D $(1,3,4)(2,6,5)(9,10)$
$S_4\times S_3^2$ 6G $6$ $12$ $D_4\times C_3^2$ 3C 2C $(2,6,5)(7,9)(8,10)$
$S_4\times S_3^2$ 6H $6$ $18$ $C_6\times D_4$ 3A 2E $(1,2,3,5,4,6)(7,8)(9,10)$
$S_4\times S_3^2$ 6I $6$ $18$ $C_6\times D_4$ 3B 2F $(1,2,3,6,4,5)(7,8)(9,10)$
$S_4\times S_3^2$ 6J $6$ $24$ $C_6^2$ 3C 2D $(2,5,6)(9,10)$
$S_4\times S_3^2$ 6K $6$ $24$ $C_6\times S_3$ 3D 2A $(1,2)(3,5)(4,6)(8,9,10)$
$S_4\times S_3^2$ 6L $6$ $24$ $C_6\times S_3$ 3D 2B $(1,2)(3,6)(4,5)(8,9,10)$
$S_4\times S_3^2$ 6M $6$ $36$ $C_2^2\times C_6$ 3B 2H $(1,2,3,6,4,5)(7,9)$
$S_4\times S_3^2$ 6N $6$ $36$ $C_2^2\times C_6$ 3A 2I $(1,6,4,5,3,2)(7,10)$
$S_4\times S_3^2$ 6O $6$ $48$ $C_3\times C_6$ 3E 2A $(1,5,3,6,4,2)(7,9,10)$
$S_4\times S_3^2$ 6P $6$ $48$ $C_3\times C_6$ 3F 2B $(1,6,4,2,3,5)(7,9,10)$
$S_4\times S_3^2$ 6Q $6$ $72$ $C_2\times C_6$ 3D 2G $(3,4)(5,6)(8,10,9)$
$S_4\times S_3^2$ 12A $12$ $12$ $S_3\times C_{12}$ 6C 4A $(1,3,4)(2,5,6)(7,8,9,10)$
$S_4\times S_3^2$ 12B $12$ $12$ $S_3\times C_{12}$ 6D 4A $(1,3,4)(2,6,5)(7,8,9,10)$
$S_4\times S_3^2$ 12C $12$ $24$ $C_3\times C_{12}$ 6G 4A $(2,5,6)(7,8,9,10)$
$S_4\times S_3^2$ 12D $12$ $36$ $C_2\times C_{12}$ 6D 4B $(1,5,4,6,3,2)(7,8,9,10)$
$S_4\times S_3^2$ 12E $12$ $36$ $C_2\times C_{12}$ 6C 4C $(1,2,3,5,4,6)(7,10,8,9)$
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