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

Group Label Order Size Centralizer Powers Representative
2P
$C_2^3.C_2^5$ 1A $1$ $1$ $C_2^3.C_2^5$ 1A $()$
$C_2^3.C_2^5$ 2A $2$ $1$ $C_2^3.C_2^5$ 1A $(17,18)$
$C_2^3.C_2^5$ 2B $2$ $1$ $C_2^3.C_2^5$ 1A $(1,5)(2,8)(3,10)(4,11)(6,12)(7,14)(9,15)(13,16)(17,18)$
$C_2^3.C_2^5$ 2C $2$ $1$ $C_2^3.C_2^5$ 1A $(1,5)(2,8)(3,10)(4,11)(6,12)(7,14)(9,15)(13,16)$
$C_2^3.C_2^5$ 2D $2$ $2$ $C_4^2:C_2^3$ 1A $(3,10)(6,12)(9,15)(13,16)(17,18)$
$C_2^3.C_2^5$ 2E $2$ $2$ $C_4^2:C_2^3$ 1A $(2,8)(6,12)(7,14)(13,16)(17,18)$
$C_2^3.C_2^5$ 2F $2$ $2$ $C_4^2:C_2^3$ 1A $(2,8)(3,10)(7,14)(9,15)(17,18)$
$C_2^3.C_2^5$ 2G $2$ $2$ $C_4^2:C_2^3$ 1A $(3,10)(6,12)(9,15)(13,16)$
$C_2^3.C_2^5$ 2H $2$ $2$ $C_4^2:C_2^3$ 1A $(2,8)(6,12)(7,14)(13,16)$
$C_2^3.C_2^5$ 2I $2$ $2$ $C_4^2:C_2^3$ 1A $(1,5)(4,11)(6,12)(13,16)$
$C_2^3.C_2^5$ 2J $2$ $4$ $C_2^4\times C_4$ 1A $(6,12)(13,16)$
$C_2^3.C_2^5$ 2K $2$ $4$ $C_2^4\times C_4$ 1A $(6,12)(13,16)(17,18)$
$C_2^3.C_2^5$ 2L $2$ $4$ $C_2^4\times C_4$ 1A $(2,8)(3,10)(6,12)(7,14)(9,15)(13,16)$
$C_2^3.C_2^5$ 2M $2$ $4$ $C_2^4\times C_4$ 1A $(2,8)(3,10)(6,12)(7,14)(9,15)(13,16)(17,18)$
$C_2^3.C_2^5$ 2N $2$ $4$ $D_4:C_2^3$ 1A $(1,2)(3,6)(4,7)(5,8)(9,13)(10,12)(11,14)(15,16)$
$C_2^3.C_2^5$ 2O $2$ $4$ $D_4:C_2^3$ 1A $(1,2)(3,6)(4,7)(5,8)(9,13)(10,12)(11,14)(15,16)(17,18)$
$C_2^3.C_2^5$ 2P $2$ $4$ $D_4:C_2^3$ 1A $(1,3)(2,6)(4,9)(5,10)(7,13)(8,12)(11,15)(14,16)$
$C_2^3.C_2^5$ 2Q $2$ $4$ $D_4:C_2^3$ 1A $(1,3)(2,6)(4,9)(5,10)(7,13)(8,12)(11,15)(14,16)(17,18)$
$C_2^3.C_2^5$ 2R $2$ $4$ $D_4:C_2^3$ 1A $(1,6)(2,3)(4,13)(5,12)(7,9)(8,10)(11,16)(14,15)$
$C_2^3.C_2^5$ 2S $2$ $4$ $D_4:C_2^3$ 1A $(1,6)(2,3)(4,13)(5,12)(7,9)(8,10)(11,16)(14,15)(17,18)$
$C_2^3.C_2^5$ 2T $2$ $4$ $D_4:C_2^3$ 1A $(1,7)(2,11)(3,13)(4,8)(5,14)(6,15)(9,12)(10,16)$
$C_2^3.C_2^5$ 2U $2$ $4$ $D_4:C_2^3$ 1A $(1,7)(2,11)(3,13)(4,8)(5,14)(6,15)(9,12)(10,16)(17,18)$
$C_2^3.C_2^5$ 2V $2$ $4$ $D_4:C_2^3$ 1A $(1,9)(2,13)(3,11)(4,10)(5,15)(6,14)(7,12)(8,16)$
$C_2^3.C_2^5$ 2W $2$ $4$ $D_4:C_2^3$ 1A $(1,9)(2,13)(3,11)(4,10)(5,15)(6,14)(7,12)(8,16)(17,18)$
$C_2^3.C_2^5$ 2X $2$ $4$ $D_4:C_2^3$ 1A $(1,13)(2,9)(3,14)(4,12)(5,16)(6,11)(7,10)(8,15)$
$C_2^3.C_2^5$ 2Y $2$ $4$ $D_4:C_2^3$ 1A $(1,13)(2,9)(3,14)(4,12)(5,16)(6,11)(7,10)(8,15)(17,18)$
$C_2^3.C_2^5$ 4A1 $4$ $1$ $C_2^3.C_2^5$ 2C $(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,13,12,16)$
$C_2^3.C_2^5$ 4A-1 $4$ $1$ $C_2^3.C_2^5$ 2C $(1,11,5,4)(2,14,8,7)(3,15,10,9)(6,16,12,13)$
$C_2^3.C_2^5$ 4B1 $4$ $1$ $C_2^3.C_2^5$ 2C $(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,13,12,16)(17,18)$
$C_2^3.C_2^5$ 4B-1 $4$ $1$ $C_2^3.C_2^5$ 2C $(1,11,5,4)(2,14,8,7)(3,15,10,9)(6,16,12,13)(17,18)$
$C_2^3.C_2^5$ 4C $4$ $2$ $C_4^2:C_2^3$ 2C $(1,4,5,11)(2,7,8,14)(3,15,10,9)(6,16,12,13)$
$C_2^3.C_2^5$ 4D $4$ $2$ $C_4^2:C_2^3$ 2C $(1,4,5,11)(2,7,8,14)(3,15,10,9)(6,16,12,13)(17,18)$
$C_2^3.C_2^5$ 4E $4$ $2$ $C_4^2:C_2^3$ 2C $(1,4,5,11)(2,14,8,7)(3,9,10,15)(6,16,12,13)$
$C_2^3.C_2^5$ 4F $4$ $2$ $C_4^2:C_2^3$ 2C $(1,4,5,11)(2,14,8,7)(3,9,10,15)(6,16,12,13)(17,18)$
$C_2^3.C_2^5$ 4G $4$ $2$ $C_4^2:C_2^3$ 2C $(1,4,5,11)(2,14,8,7)(3,15,10,9)(6,13,12,16)$
$C_2^3.C_2^5$ 4H $4$ $2$ $C_4^2:C_2^3$ 2C $(1,4,5,11)(2,14,8,7)(3,15,10,9)(6,13,12,16)(17,18)$
$C_2^3.C_2^5$ 4I $4$ $4$ $D_4:C_2^3$ 2C $(1,2,5,8)(3,6,10,12)(4,7,11,14)(9,13,15,16)$
$C_2^3.C_2^5$ 4J $4$ $4$ $D_4:C_2^3$ 2C $(1,2,5,8)(3,6,10,12)(4,7,11,14)(9,13,15,16)(17,18)$
$C_2^3.C_2^5$ 4K $4$ $4$ $D_4:C_2^3$ 2C $(1,3,5,10)(2,6,8,12)(4,9,11,15)(7,13,14,16)$
$C_2^3.C_2^5$ 4L $4$ $4$ $D_4:C_2^3$ 2C $(1,3,5,10)(2,6,8,12)(4,9,11,15)(7,13,14,16)(17,18)$
$C_2^3.C_2^5$ 4M $4$ $4$ $D_4:C_2^3$ 2C $(1,6,5,12)(2,3,8,10)(4,13,11,16)(7,9,14,15)$
$C_2^3.C_2^5$ 4N $4$ $4$ $D_4:C_2^3$ 2C $(1,6,5,12)(2,3,8,10)(4,13,11,16)(7,9,14,15)(17,18)$
$C_2^3.C_2^5$ 4O $4$ $4$ $D_4:C_2^3$ 2C $(1,7,5,14)(2,4,8,11)(3,13,10,16)(6,9,12,15)$
$C_2^3.C_2^5$ 4P $4$ $4$ $D_4:C_2^3$ 2C $(1,7,5,14)(2,4,8,11)(3,13,10,16)(6,9,12,15)(17,18)$
$C_2^3.C_2^5$ 4Q $4$ $4$ $D_4:C_2^3$ 2C $(1,9,5,15)(2,13,8,16)(3,4,10,11)(6,7,12,14)$
$C_2^3.C_2^5$ 4R $4$ $4$ $D_4:C_2^3$ 2C $(1,9,5,15)(2,13,8,16)(3,4,10,11)(6,7,12,14)(17,18)$
$C_2^3.C_2^5$ 4S $4$ $4$ $D_4:C_2^3$ 2C $(1,13,5,16)(2,9,8,15)(3,7,10,14)(4,12,11,6)$
$C_2^3.C_2^5$ 4T $4$ $4$ $D_4:C_2^3$ 2C $(1,13,5,16)(2,9,8,15)(3,7,10,14)(4,12,11,6)(17,18)$
$C_2^3.C_2^5$ 4U1 $4$ $4$ $C_2^4\times C_4$ 2C $(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,16,12,13)$
$C_2^3.C_2^5$ 4U-1 $4$ $4$ $C_2^4\times C_4$ 2C $(1,4,5,11)(2,14,8,7)(3,15,10,9)(6,16,12,13)$
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