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Results (48 matches)

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Elements of the group are displayed as permutations of degree 18.

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_2^6:S_4$ 1A $1$ $1$ $C_2^6:S_4$ 1A 1A $()$
$C_2^6:S_4$ 2A $2$ $1$ $C_2^6:S_4$ 1A 2A $(17,18)$
$C_2^6:S_4$ 2B $2$ $3$ $D_4^2:C_2^3$ 1A 2B $(1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,16)(14,15)(17,18)$
$C_2^6:S_4$ 2C $2$ $3$ $D_4^2:C_2^3$ 1A 2C $(1,6)(2,3)(4,12)(5,13)(7,9)(8,10)(11,14)(15,16)$
$C_2^6:S_4$ 2D $2$ $4$ $C_2^2\wr S_3$ 1A 2D $(4,12)(5,10)(7,9)(8,13)(11,16)(14,15)$
$C_2^6:S_4$ 2E $2$ $4$ $C_2^2\wr S_3$ 1A 2E $(4,12)(5,10)(7,9)(8,13)(11,16)(14,15)(17,18)$
$C_2^6:S_4$ 2F $2$ $6$ $C_2^5:D_4$ 1A 2F $(5,13)(8,10)(11,14)(15,16)$
$C_2^6:S_4$ 2G $2$ $6$ $C_2^5:D_4$ 1A 2G $(5,13)(8,10)(11,14)(15,16)(17,18)$
$C_2^6:S_4$ 2H $2$ $6$ $C_2^6:C_4$ 1A 2H $(1,2)(3,6)(4,7)(5,10)(8,13)(9,12)(11,15)(14,16)$
$C_2^6:S_4$ 2I $2$ $6$ $C_2^6:C_4$ 1A 2I $(1,2)(3,6)(4,7)(5,10)(8,13)(9,12)(11,15)(14,16)(17,18)$
$C_2^6:S_4$ 2J $2$ $12$ $C_2^4:D_4$ 1A 2J $(4,7)(5,10)(8,13)(9,12)(11,14)(15,16)(17,18)$
$C_2^6:S_4$ 2K $2$ $12$ $C_2^4:D_4$ 1A 2K $(1,4)(2,7)(3,9)(5,11)(6,12)(8,16)(10,15)(13,14)(17,18)$
$C_2^6:S_4$ 2L $2$ $12$ $C_2^5:C_4$ 1A 2L $(1,4)(2,7)(3,9)(5,14)(6,12)(8,15)(10,16)(11,13)$
$C_2^6:S_4$ 2M $2$ $12$ $C_2^5:C_4$ 1A 2M $(1,4)(2,7)(3,9)(5,14)(6,12)(8,15)(10,16)(11,13)(17,18)$
$C_2^6:S_4$ 2N $2$ $12$ $C_2^4:D_4$ 1A 2N $(1,8)(2,5)(3,13)(4,16)(6,10)(7,11)(9,14)(12,15)$
$C_2^6:S_4$ 2O $2$ $12$ $C_2^4:D_4$ 1A 2O $(1,2)(3,6)(5,13)(8,10)(11,15)(14,16)$
$C_2^6:S_4$ 2P $2$ $24$ $D_4\times C_2^3$ 1A 2P $(3,6)(4,5)(7,8)(9,13)(10,12)(14,15)$
$C_2^6:S_4$ 2Q $2$ $24$ $D_4\times C_2^3$ 1A 2Q $(3,6)(4,5)(7,8)(9,13)(10,12)(14,15)(17,18)$
$C_2^6:S_4$ 2R $2$ $24$ $D_4\times C_2^3$ 1A 2R $(3,6)(4,8)(5,7)(9,10)(12,13)(14,15)$
$C_2^6:S_4$ 2S $2$ $24$ $D_4\times C_2^3$ 1A 2S $(3,6)(4,8)(5,7)(9,10)(12,13)(14,15)(17,18)$
$C_2^6:S_4$ 3A $3$ $128$ $C_2\times C_6$ 3A 1A $(2,6,3)(4,13,14)(5,16,7)(8,15,12)(9,10,11)$
$C_2^6:S_4$ 4A $4$ $12$ $D_8:C_2^3$ 2C 4A $(1,4,6,12)(2,7,3,9)(5,15,13,16)(8,14,10,11)$
$C_2^6:S_4$ 4B $4$ $12$ $D_8:C_2^3$ 2C 4B $(1,4,6,12)(2,7,3,9)(5,15,13,16)(8,14,10,11)(17,18)$
$C_2^6:S_4$ 4C $4$ $12$ $C_4^2:C_2^3$ 2C 4C $(1,4,6,12)(2,7,3,9)(5,16,13,15)(8,11,10,14)(17,18)$
$C_2^6:S_4$ 4D $4$ $12$ $C_4^2:C_2^3$ 2C 4D $(1,5,3,10)(2,8,6,13)(4,16,9,14)(7,11,12,15)$
$C_2^6:S_4$ 4E $4$ $24$ $D_4:C_2^3$ 2C 4E $(1,2,3,6)(4,11,9,15)(5,13,10,8)(7,14,12,16)$
$C_2^6:S_4$ 4F $4$ $24$ $D_4:C_2^3$ 2C 4F $(1,2,3,6)(4,11,9,15)(5,13,10,8)(7,14,12,16)(17,18)$
$C_2^6:S_4$ 4G $4$ $24$ $D_4:C_2^3$ 2C 4G $(1,2,3,6)(4,15,9,11)(5,13,10,8)(7,16,12,14)$
$C_2^6:S_4$ 4H $4$ $24$ $D_4:C_2^3$ 2C 4H $(1,2,3,6)(4,15,9,11)(5,13,10,8)(7,16,12,14)(17,18)$
$C_2^6:S_4$ 4I $4$ $24$ $C_4^2:C_2^2$ 2C 4I $(1,4,2,7)(3,9,6,12)(5,15,8,14)(10,11,13,16)$
$C_2^6:S_4$ 4J $4$ $24$ $C_4^2:C_2^2$ 2C 4J $(1,4,2,7)(3,9,6,12)(5,15,8,14)(10,11,13,16)(17,18)$
$C_2^6:S_4$ 4K $4$ $24$ $C_4^2:C_2^2$ 2C 4K $(1,4,2,7)(3,9,6,12)(5,16,8,11)(10,14,13,15)$
$C_2^6:S_4$ 4L $4$ $24$ $C_4^2:C_2^2$ 2C 4L $(1,4,2,7)(3,9,6,12)(5,16,8,11)(10,14,13,15)(17,18)$
$C_2^6:S_4$ 4M $4$ $48$ $C_2^3\times C_4$ 2N 4M $(1,12,8,15)(2,4,5,16)(3,7,13,11)(6,9,10,14)$
$C_2^6:S_4$ 4N $4$ $48$ $C_2^3\times C_4$ 2O 4N $(1,10,2,8)(3,5,6,13)(4,9)(11,14,15,16)$
$C_2^6:S_4$ 4O $4$ $48$ $C_2^3\times C_4$ 2N 4O $(1,14,8,9)(2,11,5,7)(3,16,13,4)(6,15,10,12)(17,18)$
$C_2^6:S_4$ 4P $4$ $48$ $C_2^3\times C_4$ 2O 4P $(1,2)(4,5,9,13)(7,8,12,10)(11,14,16,15)(17,18)$
$C_2^6:S_4$ 4Q $4$ $48$ $C_2^3\times C_4$ 2O 4Q $(1,6)(4,9,12,7)(5,11,8,15)(10,16,13,14)$
$C_2^6:S_4$ 4R $4$ $48$ $C_2^3\times C_4$ 2N 4R $(1,15,13,7)(2,16,10,9)(3,11,8,12)(4,6,14,5)$
$C_2^6:S_4$ 4S $4$ $48$ $C_2^3\times C_4$ 2O 4S $(1,5,6,8)(2,13,3,10)(4,12,9,7)(14,16)(17,18)$
$C_2^6:S_4$ 4T $4$ $48$ $C_2^3\times C_4$ 2N 4T $(1,11,8,7)(2,14,5,9)(3,15,13,12)(4,6,16,10)(17,18)$
$C_2^6:S_4$ 6A $6$ $128$ $C_2\times C_6$ 3A 2A $(2,3,6)(4,14,13)(5,7,16)(8,12,15)(9,11,10)(17,18)$
$C_2^6:S_4$ 6B $6$ $128$ $C_2\times C_6$ 3A 2D $(1,3,2)(4,11,10,12,16,5)(7,15,8,9,14,13)$
$C_2^6:S_4$ 6C $6$ $128$ $C_2\times C_6$ 3A 2E $(1,6,2)(4,8,16,12,13,11)(5,15,7,10,14,9)(17,18)$
$C_2^6:S_4$ 8A $8$ $48$ $C_2^2\times C_8$ 4D 8A $(1,4,5,16,3,9,10,14)(2,12,8,15,6,7,13,11)(17,18)$
$C_2^6:S_4$ 8B $8$ $48$ $C_2^2\times C_8$ 4D 8B $(1,15,13,9,3,11,8,4)(2,16,10,7,6,14,5,12)(17,18)$
$C_2^6:S_4$ 8C $8$ $48$ $C_2^2\times C_8$ 4D 8C $(1,14,10,9,3,16,5,4)(2,11,13,7,6,15,8,12)$
$C_2^6:S_4$ 8D $8$ $48$ $C_2^2\times C_8$ 4D 8D $(1,11,13,4,3,15,8,9)(2,14,10,12,6,16,5,7)$
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