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Results (34 matches)

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Elements of the group are displayed as permutations of degree 16.

Group Label Order Size Centralizer Powers Representative
2P
$C_2^4.C_2\wr C_4$ 1A $1$ $1$ $C_2^4.C_2\wr C_4$ 1A $()$
$C_2^4.C_2\wr C_4$ 2A $2$ $1$ $C_2^4.C_2\wr C_4$ 1A $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$
$C_2^4.C_2\wr C_4$ 2B $2$ $2$ $C_2^6:D_4$ 1A $(9,10)(11,12)(13,14)(15,16)$
$C_2^4.C_2\wr C_4$ 2C $2$ $4$ $C_2^6:C_2^2$ 1A $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$
$C_2^4.C_2\wr C_4$ 2D $2$ $4$ $C_2^6:C_2^2$ 1A $(5,6)(7,8)$
$C_2^4.C_2\wr C_4$ 2E $2$ $4$ $C_2^6:C_2^2$ 1A $(5,6)(7,8)(13,14)(15,16)$
$C_2^4.C_2\wr C_4$ 2F $2$ $8$ $C_2^3\wr C_2$ 1A $(1,4)(2,3)(5,7)(6,8)(9,10)(15,16)$
$C_2^4.C_2\wr C_4$ 2G $2$ $8$ $C_2^3\wr C_2$ 1A $(1,4)(2,3)(5,8)(6,7)(9,10)(13,14)$
$C_2^4.C_2\wr C_4$ 2H $2$ $16$ $C_2^6$ 1A $(7,8)(9,11)(10,12)$
$C_2^4.C_2\wr C_4$ 2I $2$ $16$ $C_2^6$ 1A $(7,8)(9,11)(10,12)(13,14)(15,16)$
$C_2^4.C_2\wr C_4$ 2J $2$ $16$ $C_2^6$ 1A $(5,7)(6,8)(9,10)(11,12)(15,16)$
$C_2^4.C_2\wr C_4$ 2K $2$ $16$ $C_2^6$ 1A $(3,4)(7,8)(9,11)(10,12)(13,15)(14,16)$
$C_2^4.C_2\wr C_4$ 2L $2$ $16$ $C_2^6$ 1A $(3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)$
$C_2^4.C_2\wr C_4$ 2M $2$ $16$ $C_2^3.D_4$ 1A $(1,6)(2,5)(3,7)(4,8)(9,15)(10,16)(11,14)(12,13)$
$C_2^4.C_2\wr C_4$ 4A $4$ $8$ $(C_2^3\times C_4):C_4$ 2A $(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,16,14,15)$
$C_2^4.C_2\wr C_4$ 4B $4$ $8$ $C_2^4.C_8$ 2A $(1,3,2,4)(5,8,6,7)(9,11,10,12)(13,16,14,15)$
$C_2^4.C_2\wr C_4$ 4C $4$ $16$ $C_4^2:C_2^2$ 2A $(1,7,2,8)(3,6,4,5)(9,16,10,15)(11,14,12,13)$
$C_2^4.C_2\wr C_4$ 4D $4$ $32$ $C_2^3\times C_4$ 2D $(5,7,6,8)(9,11)(10,12)(15,16)$
$C_2^4.C_2\wr C_4$ 4E $4$ $32$ $C_2^3\times C_4$ 2D $(3,4)(5,7)(6,8)(9,10)(11,12)(13,15,14,16)$
$C_2^4.C_2\wr C_4$ 4F $4$ $32$ $C_2^3\times C_4$ 2E $(3,4)(5,7,6,8)(9,11)(10,12)(13,15,14,16)$
$C_2^4.C_2\wr C_4$ 4G $4$ $32$ $C_2^3\times C_4$ 2E $(3,4)(5,7,6,8)(9,12)(10,11)(13,15,14,16)$
$C_2^4.C_2\wr C_4$ 4H $4$ $32$ $C_4\times D_4$ 2B $(1,5)(2,6)(3,7)(4,8)(9,13,10,14)(11,16,12,15)$
$C_2^4.C_2\wr C_4$ 4I $4$ $64$ $C_2^2\times C_4$ 2F $(1,6,4,8)(2,5,3,7)(9,15,10,16)(11,14)(12,13)$
$C_2^4.C_2\wr C_4$ 4J $4$ $64$ $C_2^2\times C_4$ 2G $(1,8,4,5)(2,7,3,6)(9,13,10,14)(11,15)(12,16)$
$C_2^4.C_2\wr C_4$ 4K1 $4$ $64$ $C_4^2$ 2M $(1,12,6,13)(2,11,5,14)(3,10,7,16)(4,9,8,15)$
$C_2^4.C_2\wr C_4$ 4K-1 $4$ $64$ $C_4^2$ 2M $(1,13,6,12)(2,14,5,11)(3,16,7,10)(4,15,8,9)$
$C_2^4.C_2\wr C_4$ 8A1 $8$ $32$ $\OD_{32}$ 4B $(1,6,3,7,2,5,4,8)(9,13,11,16,10,14,12,15)$
$C_2^4.C_2\wr C_4$ 8A-1 $8$ $32$ $\OD_{32}$ 4B $(1,8,4,5,2,7,3,6)(9,15,12,14,10,16,11,13)$
$C_2^4.C_2\wr C_4$ 8B1 $8$ $64$ $C_2\times C_8$ 4C $(1,14,7,12,2,13,8,11)(3,16,6,10,4,15,5,9)$
$C_2^4.C_2\wr C_4$ 8B-1 $8$ $64$ $C_2\times C_8$ 4C $(1,11,8,13,2,12,7,14)(3,9,5,15,4,10,6,16)$
$C_2^4.C_2\wr C_4$ 16A1 $16$ $64$ $C_{16}$ 8A1 $(1,14,6,12,3,15,7,9,2,13,5,11,4,16,8,10)$
$C_2^4.C_2\wr C_4$ 16A-1 $16$ $64$ $C_{16}$ 8A-1 $(1,10,8,16,4,11,5,13,2,9,7,15,3,12,6,14)$
$C_2^4.C_2\wr C_4$ 16A3 $16$ $64$ $C_{16}$ 8A-1 $(1,12,7,13,4,10,6,15,2,11,8,14,3,9,5,16)$
$C_2^4.C_2\wr C_4$ 16A-3 $16$ $64$ $C_{16}$ 8A1 $(1,16,5,9,3,14,8,11,2,15,6,10,4,13,7,12)$
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