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Elements of the group are displayed as permutations of degree 24.

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_2^8.C_2^3:S_4$ 1A $1$ $1$ $C_2^8.C_2^3:S_4$ 1A 1A $()$
$C_2^8.C_2^3:S_4$ 2A $2$ $1$ $C_2^8.C_2^3:S_4$ 1A 2A $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2B $2$ $2$ $C_2^8.C_2^4.C_6$ 1A 2B $(5,6)(7,8)(13,14)(15,16)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2C $2$ $3$ $C_2^7.C_2^6.C_2$ 1A 2C $(13,14)(15,16)(17,18)(19,20)$
$C_2^8.C_2^3:S_4$ 2D $2$ $3$ $C_2^7.C_2^6.C_2$ 1A 2D $(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2E $2$ $3$ $C_2^7.C_2^6.C_2$ 1A 2E $(9,10)(11,12)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2F $2$ $3$ $C_2^7.C_2^6.C_2$ 1A 2F $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$
$C_2^8.C_2^3:S_4$ 2G $2$ $3$ $C_2^7.C_2^6.C_2$ 1A 2G $(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2H $2$ $3$ $C_2^7.C_2^6.C_2$ 1A 2H $(1,2)(3,4)(5,6)(7,8)(13,14)(15,16)(17,18)(19,20)$
$C_2^8.C_2^3:S_4$ 2I $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2I $(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2J $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2J $(5,6)(7,8)(13,14)(15,16)(17,18)(19,20)$
$C_2^8.C_2^3:S_4$ 2K $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2K $(5,6)(7,8)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2L $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2L $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2M $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2M $(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2N $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2N $(13,14)(15,16)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2O $2$ $6$ $C_2^6.C_2^6.C_2$ 1A 2O $(9,10)(11,12)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2P $2$ $24$ $C_2.C_2^6.C_2^4$ 1A 2P $(7,8)(9,11)(10,12)(13,15)(14,16)(19,20)$
$C_2^8.C_2^3:S_4$ 2Q $2$ $24$ $C_2.C_2^6.C_2^4$ 1A 2Q $(7,8)(9,11)(10,12)(13,15)(14,16)(17,18)$
$C_2^8.C_2^3:S_4$ 2R $2$ $24$ $C_2.C_2^6.C_2^4$ 1A 2R $(3,4)(5,6)(7,8)(9,10)(11,12)(15,16)(17,19)(18,20)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2S $2$ $24$ $C_2.C_2^6.C_2^4$ 1A 2S $(3,4)(5,6)(7,8)(9,10)(11,12)(15,16)(17,19)(18,20)(21,24)(22,23)$
$C_2^8.C_2^3:S_4$ 2T $2$ $48$ not computed 1A 2T $(11,12)(13,15)(14,16)(17,19)(18,20)(23,24)$
$C_2^8.C_2^3:S_4$ 2U $2$ $48$ not computed 1A 2U $(7,8)(11,12)(17,19)(18,20)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2V $2$ $48$ not computed 1A 2V $(7,8)(9,11)(10,12)(13,15)(14,16)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2W $2$ $48$ not computed 1A 2W $(7,8)(9,11)(10,12)(13,15)(14,16)(17,18)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2X $2$ $48$ not computed 1A 2X $(5,7)(6,8)(11,12)(15,16)(17,19)(18,20)$
$C_2^8.C_2^3:S_4$ 2Y $2$ $48$ not computed 1A 2Y $(3,4)(7,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2Z $2$ $48$ not computed 1A 2Z $(3,4)(5,6)(7,8)(9,11)(10,12)(13,15)(14,16)(17,18)(19,20)(23,24)$
$C_2^8.C_2^3:S_4$ 2AA $2$ $48$ not computed 1A 2AA $(3,4)(5,7)(6,8)(9,11)(10,12)(15,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2AB $2$ $48$ not computed 1A 2AB $(5,7)(6,8)(9,12)(10,11)(17,20)(18,19)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2AC $2$ $48$ not computed 1A 2AC $(1,2)(3,4)(5,8)(6,7)(9,11)(10,12)(13,14)(15,16)(17,20)(18,19)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2AD $2$ $48$ not computed 1A 2AD $(1,2)(3,4)(5,6)(7,8)(11,12)(13,14)(17,18)(21,22)$
$C_2^8.C_2^3:S_4$ 2AE $2$ $48$ not computed 1A 2AE $(3,4)(7,8)(19,20)(23,24)$
$C_2^8.C_2^3:S_4$ 2AF $2$ $96$ not computed 1A 2AF $(7,8)(11,12)(13,14)(15,16)(17,19)(18,20)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2AG $2$ $96$ not computed 1A 2AG $(7,8)(9,11)(10,12)(15,16)(17,19)(18,20)$
$C_2^8.C_2^3:S_4$ 2AH $2$ $96$ not computed 1A 2AH $(7,8)(9,11)(10,12)(15,16)(17,19)(18,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2AI $2$ $96$ not computed 1A 2AI $(5,6)(7,8)(11,12)(15,16)(19,20)(23,24)$
$C_2^8.C_2^3:S_4$ 2AJ $2$ $96$ not computed 1A 2AJ $(5,6)(7,8)(11,12)(13,15)(14,16)(17,19)(18,20)(23,24)$
$C_2^8.C_2^3:S_4$ 2AK $2$ $96$ not computed 1A 2AK $(5,7)(6,8)(11,12)(15,16)(17,19)(18,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2AL $2$ $96$ not computed 1A 2AL $(5,7)(6,8)(11,12)(13,15)(14,16)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 2AM $2$ $96$ not computed 1A 2AM $(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)(17,19)(18,20)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2AN $2$ $96$ not computed 1A 2AN $(3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)(19,20)(21,23)(22,24)$
$C_2^8.C_2^3:S_4$ 2AO $2$ $192$ not computed 1A 2AO $(1,5)(2,6)(3,7)(4,8)(9,23)(10,24)(11,21)(12,22)(13,17)(14,18)(15,19)(16,20)$
$C_2^8.C_2^3:S_4$ 2AP $2$ $192$ not computed 1A 2AP $(1,5)(2,6)(3,7)(4,8)(9,23)(10,24)(11,21)(12,22)(13,19)(14,20)(15,18)(16,17)$
$C_2^8.C_2^3:S_4$ 3A $3$ $2048$ not computed 3A 1A $(1,11,17)(2,12,18)(3,10,19)(4,9,20)(5,14,23)(6,13,24)(7,15,21)(8,16,22)$
$C_2^8.C_2^3:S_4$ 4A $4$ $12$ $C_2^5.C_2^3.C_2^4$ 2C 4A $(13,15,14,16)(17,19,18,20)$
$C_2^8.C_2^3:S_4$ 4B $4$ $12$ $C_2^5.C_2^3.C_2^4$ 2C 4B $(9,10)(11,12)(13,15,14,16)(17,19,18,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 4C $4$ $12$ $C_2^5.C_2^3.C_2^4$ 2C 4C $(5,7,6,8)(9,11,10,12)(17,18)(19,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 4D $4$ $12$ $C_2^5.C_2^3.C_2^4$ 2C 4D $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,15,14,16)(17,19,18,20)(21,22)(23,24)$
$C_2^8.C_2^3:S_4$ 4E1 $4$ $16$ $(C_2\times C_4^3):S_4$ 2A 4E-1 $(1,3,2,4)(5,8,6,7)(9,12,10,11)(13,16,14,15)(17,20,18,19)(21,24,22,23)$
$C_2^8.C_2^3:S_4$ 4E-1 $4$ $16$ $(C_2\times C_4^3):S_4$ 2A 4E1 $(1,4,2,3)(5,7,6,8)(9,11,10,12)(13,15,14,16)(17,19,18,20)(21,23,22,24)$
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