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

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_2^9.A_4^3:S_4$ 1A $1$ $1$ $C_2^9.A_4^3:S_4$ 1A 1A $()$
$C_2^9.A_4^3:S_4$ 2A $2$ $9$ $C_2^8.C_3^2.C_2^5.C_2^5$ 1A 2A $(17,18)(19,20)(21,22)(23,24)$
$C_2^9.A_4^3:S_4$ 2B $2$ $12$ $C_2^8.C_6^2.C_6.C_2.C_2^4$ 1A 2B $(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2C $2$ $18$ $C_2^8.C_3^2.C_2^5.C_2^4$ 1A 2C $(13,14)(15,16)$
$C_2^9.A_4^3:S_4$ 2D $2$ $18$ $C_2^8.C_3^2.C_2^5.C_2^4$ 1A 2D $(17,19)(18,20)(21,24)(22,23)$
$C_2^9.A_4^3:S_4$ 2E $2$ $27$ $C_2^9.C_2^6.C_6.C_2^2$ 1A 2E $(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2F $2$ $27$ $C_2^8.C_6.C_2^5.C_2^4$ 1A 2F $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,18)(19,20)(21,22)(23,24)$
$C_2^9.A_4^3:S_4$ 2G $2$ $48$ not computed 1A 2G $(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2H $2$ $64$ $A_4^3.C_2^3:S_4$ 1A 2H $(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2I $2$ $72$ not computed 1A 2I $(9,10)(11,12)(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2J $2$ $108$ not computed 1A 2J $(5,6)(7,8)(17,19)(18,20)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2K $2$ $108$ not computed 1A 2K $(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,24)(22,23)$
$C_2^9.A_4^3:S_4$ 2L $2$ $108$ not computed 1A 2L $(13,14)(15,16)(21,22)(23,24)$
$C_2^9.A_4^3:S_4$ 2M $2$ $108$ not computed 1A 2M $(9,11)(10,12)(13,16)(14,15)(17,19)(18,20)(21,24)(22,23)$
$C_2^9.A_4^3:S_4$ 2N $2$ $108$ not computed 1A 2N $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2O $2$ $144$ not computed 1A 2O $(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2P $2$ $144$ not computed 1A 2P $(9,10)(11,12)(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2Q $2$ $144$ not computed 1A 2Q $(1,2)(3,4)(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2R $2$ $162$ not computed 1A 2R $(1,3)(2,4)(5,7)(6,8)(9,12)(10,11)(13,16)(14,15)(21,22)(23,24)$
$C_2^9.A_4^3:S_4$ 2S $2$ $162$ not computed 1A 2S $(1,2)(3,4)(5,7)(6,8)(9,12)(10,11)(13,16)(14,15)(17,19)(18,20)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2T $2$ $216$ not computed 1A 2T $(5,6)(7,8)(17,19)(18,20)(21,24)(22,23)$
$C_2^9.A_4^3:S_4$ 2U $2$ $216$ not computed 1A 2U $(1,4)(2,3)(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,24)(22,23)$
$C_2^9.A_4^3:S_4$ 2V $2$ $216$ not computed 1A 2V $(5,7)(6,8)(9,12)(10,11)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2W $2$ $288$ not computed 1A 2W $(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2X $2$ $288$ not computed 1A 2X $(1,2)(3,4)(5,7)(6,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2Y $2$ $324$ not computed 1A 2Y $(1,3)(2,4)(5,8)(6,7)(9,11)(10,12)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)$
$C_2^9.A_4^3:S_4$ 2Z $2$ $324$ not computed 1A 2Z $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)$
$C_2^9.A_4^3:S_4$ 2AA $2$ $432$ not computed 1A 2AA $(5,6)(7,8)(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2AB $2$ $432$ not computed 1A 2AB $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2AC $2$ $432$ not computed 1A 2AC $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2AD $2$ $432$ not computed 1A 2AD $(1,2)(3,4)(5,7)(6,8)(9,10)(11,12)(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2AE $2$ $432$ not computed 1A 2AE $(9,14)(10,16)(11,13)(12,15)(17,24)(18,21)(19,22)(20,23)$
$C_2^9.A_4^3:S_4$ 2AF $2$ $432$ not computed 1A 2AF $(2,3)(6,7)(18,20)(22,24)$
$C_2^9.A_4^3:S_4$ 2AG $2$ $648$ not computed 1A 2AG $(1,3)(2,4)(5,8)(6,7)(13,15)(14,16)(17,20)(18,19)$
$C_2^9.A_4^3:S_4$ 2AH $2$ $648$ not computed 1A 2AH $(5,8)(6,7)(9,10)(11,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2AI $2$ $648$ not computed 1A 2AI $(1,2)(3,4)(5,7)(6,8)(9,10)(11,12)(13,15)(14,16)(17,18)(19,20)$
$C_2^9.A_4^3:S_4$ 2AJ $2$ $864$ not computed 1A 2AJ $(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)$
$C_2^9.A_4^3:S_4$ 2AK $2$ $864$ not computed 1A 2AK $(3,4)(5,6)(9,13)(10,14)(11,16)(12,15)$
$C_2^9.A_4^3:S_4$ 2AL $2$ $1296$ not computed 1A 2AL $(1,3)(2,4)(5,7)(6,8)(9,13)(10,15)(11,14)(12,16)(17,22)(18,23)(19,24)(20,21)$
$C_2^9.A_4^3:S_4$ 2AM $2$ $1296$ not computed 1A 2AM $(1,4)(6,7)(9,12)(14,15)(17,19)(18,20)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2AN $2$ $1728$ not computed 1A 2AN $(1,5)(2,8)(3,7)(4,6)(9,15)(10,16)(11,14)(12,13)(17,24)(18,23)(19,22)(20,21)$
$C_2^9.A_4^3:S_4$ 2AO $2$ $1728$ not computed 1A 2AO $(1,4)(6,7)(9,15)(10,16)(11,13)(12,14)(17,20)(21,24)$
$C_2^9.A_4^3:S_4$ 2AP $2$ $2592$ not computed 1A 2AP $(5,6)(7,8)(11,12)(15,16)(19,20)(23,24)$
$C_2^9.A_4^3:S_4$ 2AQ $2$ $2592$ not computed 1A 2AQ $(5,6)(7,8)(9,13)(10,14)(11,16)(12,15)(17,21)(18,22)(19,24)(20,23)$
$C_2^9.A_4^3:S_4$ 2AR $2$ $2592$ not computed 1A 2AR $(3,4)(7,8)(11,12)(15,16)(17,18)(19,20)(21,23)(22,24)$
$C_2^9.A_4^3:S_4$ 2AS $2$ $2592$ not computed 1A 2AS $(3,4)(7,8)(9,10)(11,12)(13,14)(15,16)(17,21)(18,22)(19,24)(20,23)$
$C_2^9.A_4^3:S_4$ 2AT $2$ $2592$ not computed 1A 2AT $(1,2)(3,4)(5,7)(6,8)(9,13)(10,14)(11,16)(12,15)(17,21)(18,22)(19,24)(20,23)$
$C_2^9.A_4^3:S_4$ 2AU $2$ $3456$ not computed 1A 2AU $(2,4)(6,8)(9,14)(10,13)(11,16)(12,15)(17,24)(18,22)(19,23)(20,21)$
$C_2^9.A_4^3:S_4$ 2AV $2$ $5184$ not computed 1A 2AV $(5,6)(7,8)(11,12)(15,16)(17,21)(18,22)(19,24)(20,23)$
$C_2^9.A_4^3:S_4$ 2AW $2$ $5184$ not computed 1A 2AW $(3,4)(7,8)(9,10)(11,12)(13,15)(14,16)(17,21)(18,22)(19,24)(20,23)$
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