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Elements of the group are displayed as permutations of degree 15.

Group Label Order Size Centralizer Powers Representative
2P 3P
$S_3^5:C_2^2$ 1A $1$ $1$ $S_3^5:C_2^2$ 1A 1A $()$
$S_3^5:C_2^2$ 2A $2$ $3$ $S_3^4:C_2^3$ 1A 2A $(2,3)$
$S_3^5:C_2^2$ 2B $2$ $6$ $S_3^2:D_6^2$ 1A 2B $(11,12)$
$S_3^5:C_2^2$ 2C $2$ $6$ $S_3^2:D_6^2$ 1A 2C $(10,14)(11,15)(12,13)$
$S_3^5:C_2^2$ 2D $2$ $6$ $S_3^2:D_6^2$ 1A 2D $(5,6)$
$S_3^5:C_2^2$ 2E $2$ $6$ $S_3^2:D_6^2$ 1A 2E $(4,8)(5,9)(6,7)$
$S_3^5:C_2^2$ 2F $2$ $9$ $D_4\times S_3^3:C_2$ 1A 2F $(11,12)(14,15)$
$S_3^5:C_2^2$ 2G $2$ $9$ $D_4\times S_3^3:C_2$ 1A 2G $(5,6)(8,9)$
$S_3^5:C_2^2$ 2H $2$ $18$ $D_6^2:D_6$ 1A 2H $(2,3)(11,12)$
$S_3^5:C_2^2$ 2I $2$ $18$ $D_6^2:D_6$ 1A 2I $(2,3)(10,14)(11,15)(12,13)$
$S_3^5:C_2^2$ 2J $2$ $18$ $D_6^2:D_6$ 1A 2J $(2,3)(5,6)$
$S_3^5:C_2^2$ 2K $2$ $18$ $D_6^2:D_6$ 1A 2K $(2,3)(4,8)(5,9)(6,7)$
$S_3^5:C_2^2$ 2L $2$ $27$ $D_6^2:C_2^3$ 1A 2L $(2,3)(11,12)(14,15)$
$S_3^5:C_2^2$ 2M $2$ $27$ $D_6^2:C_2^3$ 1A 2M $(2,3)(5,6)(8,9)$
$S_3^5:C_2^2$ 2N $2$ $36$ $S_3\times D_6^2$ 1A 2N $(8,9)(11,12)$
$S_3^5:C_2^2$ 2O $2$ $36$ $S_3\times D_6^2$ 1A 2O $(8,9)(10,14)(11,15)(12,13)$
$S_3^5:C_2^2$ 2P $2$ $36$ $S_3\times D_6^2$ 1A 2P $(4,7)(5,8)(6,9)(11,12)$
$S_3^5:C_2^2$ 2Q $2$ $36$ $S_3\times D_6^2$ 1A 2Q $(4,7)(5,8)(6,9)(10,14)(11,15)(12,13)$
$S_3^5:C_2^2$ 2R $2$ $54$ $C_4:D_6^2$ 1A 2R $(5,6)(8,9)(11,12)$
$S_3^5:C_2^2$ 2S $2$ $54$ $C_4:D_6^2$ 1A 2S $(5,6)(8,9)(10,14)(11,15)(12,13)$
$S_3^5:C_2^2$ 2T $2$ $54$ $C_4:D_6^2$ 1A 2T $(5,6)(11,12)(14,15)$
$S_3^5:C_2^2$ 2U $2$ $54$ $C_4:D_6^2$ 1A 2U $(4,8)(5,9)(6,7)(11,12)(14,15)$
$S_3^5:C_2^2$ 2V $2$ $81$ $S_3\times D_4^2$ 1A 2V $(4,6)(7,8)(11,12)(13,14)$
$S_3^5:C_2^2$ 2W $2$ $108$ not computed 1A 2W $(2,3)(4,5)(10,14)(11,15)(12,13)$
$S_3^5:C_2^2$ 2X $2$ $108$ not computed 1A 2X $(1,3)(4,8)(5,9)(6,7)(10,13)(11,15)(12,14)$
$S_3^5:C_2^2$ 2Y $2$ $108$ not computed 1A 2Y $(1,3)(4,9)(5,7)(6,8)(10,11)$
$S_3^5:C_2^2$ 2Z $2$ $108$ not computed 1A 2Z $(2,3)(4,5)(11,12)$
$S_3^5:C_2^2$ 2AA $2$ $162$ not computed 1A 2AA $(1,2)(4,7)(5,9)(6,8)(10,12)(13,14)$
$S_3^5:C_2^2$ 2AB $2$ $162$ not computed 1A 2AB $(2,3)(4,6)(7,9)(10,14)(11,13)(12,15)$
$S_3^5:C_2^2$ 2AC $2$ $162$ not computed 1A 2AC $(1,3)(5,6)(8,9)(11,12)$
$S_3^5:C_2^2$ 2AD $2$ $162$ not computed 1A 2AD $(1,3)(7,8)(10,11)(14,15)$
$S_3^5:C_2^2$ 2AE $2$ $243$ $C_2\times D_4^2$ 1A 2AE $(1,2)(5,6)(8,9)(10,11)(14,15)$
$S_3^5:C_2^2$ 3A $3$ $2$ $C_3^5:D_4^2$ 3A 1A $(1,3,2)$
$S_3^5:C_2^2$ 3B $3$ $4$ $S_3^4:C_6$ 3B 1A $(13,15,14)$
$S_3^5:C_2^2$ 3C $3$ $4$ $S_3^4:C_6$ 3C 1A $(10,11,12)(13,14,15)$
$S_3^5:C_2^2$ 3D $3$ $4$ $S_3^4:C_6$ 3D 1A $(7,9,8)$
$S_3^5:C_2^2$ 3E $3$ $4$ $S_3^4:C_6$ 3E 1A $(4,5,6)(7,8,9)$
$S_3^5:C_2^2$ 3F $3$ $8$ $C_3\times S_3^3:C_6$ 3F 1A $(1,3,2)(13,15,14)$
$S_3^5:C_2^2$ 3G $3$ $8$ $C_3\times S_3^3:C_6$ 3G 1A $(1,3,2)(10,11,12)(13,14,15)$
$S_3^5:C_2^2$ 3H $3$ $8$ $C_3\times S_3^3:C_6$ 3H 1A $(1,3,2)(7,9,8)$
$S_3^5:C_2^2$ 3I $3$ $8$ $C_3\times S_3^3:C_6$ 3I 1A $(1,3,2)(4,5,6)(7,8,9)$
$S_3^5:C_2^2$ 3J $3$ $16$ $C_3^2\times S_3^3$ 3J 1A $(7,9,8)(13,15,14)$
$S_3^5:C_2^2$ 3K $3$ $16$ $C_3^2\times S_3^3$ 3K 1A $(7,9,8)(10,11,12)(13,14,15)$
$S_3^5:C_2^2$ 3L $3$ $16$ $C_3^2\times S_3^3$ 3L 1A $(4,6,5)(7,9,8)(13,15,14)$
$S_3^5:C_2^2$ 3M $3$ $16$ $C_3^2\times S_3^3$ 3M 1A $(4,6,5)(7,9,8)(10,11,12)(13,14,15)$
$S_3^5:C_2^2$ 3N $3$ $32$ $C_3^3\times S_3^2$ 3N 1A $(1,3,2)(7,9,8)(13,15,14)$
$S_3^5:C_2^2$ 3O $3$ $32$ $C_3^3\times S_3^2$ 3O 1A $(1,3,2)(7,9,8)(10,11,12)(13,14,15)$
$S_3^5:C_2^2$ 3P $3$ $32$ $C_3^3\times S_3^2$ 3P 1A $(1,3,2)(4,6,5)(7,9,8)(13,15,14)$
$S_3^5:C_2^2$ 3Q $3$ $32$ $C_3^3\times S_3^2$ 3Q 1A $(1,3,2)(4,6,5)(7,9,8)(10,11,12)(13,14,15)$
$S_3^5:C_2^2$ 4A $4$ $18$ $C_4\times S_3^3:C_2$ 2F 4A $(10,13)(11,15,12,14)$
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