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

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_3^2:S_3\times S_6$ 1A $1$ $1$ $C_3^2:S_3\times S_6$ 1A 1A 1A $()$
$C_3^2:S_3\times S_6$ 2A $2$ $9$ $C_6\times S_6$ 1A 2A 2A $(7,12)(8,10)(9,11)$
$C_3^2:S_3\times S_6$ 2B $2$ $15$ $C_3^2:D_6\times S_4$ 1A 2B 2B $(5,6)$
$C_3^2:S_3\times S_6$ 2C $2$ $15$ $C_3^2:D_6\times S_4$ 1A 2C 2C $(1,2)(3,4)(5,6)$
$C_3^2:S_3\times S_6$ 2D $2$ $45$ $C_2\times C_6^2:D_6$ 1A 2D 2D $(3,5)(4,6)$
$C_3^2:S_3\times S_6$ 2E $2$ $135$ $C_2\times C_6\times S_4$ 1A 2E 2E $(5,6)(10,15)(11,13)(12,14)$
$C_3^2:S_3\times S_6$ 2F $2$ $135$ $C_2\times C_6\times S_4$ 1A 2F 2F $(1,2)(3,4)(5,6)(10,15)(11,13)(12,14)$
$C_3^2:S_3\times S_6$ 2G $2$ $405$ $C_{12}:C_2^3$ 1A 2G 2G $(1,3)(2,6)(7,10)(8,11)(9,12)$
$C_3^2:S_3\times S_6$ 3A1 $3$ $1$ $C_3^2:S_3\times S_6$ 3A-1 1A 3A-1 $(7,9,8)(10,12,11)(13,15,14)$
$C_3^2:S_3\times S_6$ 3A-1 $3$ $1$ $C_3^2:S_3\times S_6$ 3A1 1A 3A1 $(7,8,9)(10,11,12)(13,14,15)$
$C_3^2:S_3\times S_6$ 3B $3$ $6$ $C_3^2\times S_6$ 3B 1A 3B $(10,12,11)(13,14,15)$
$C_3^2:S_3\times S_6$ 3C $3$ $6$ $C_3^2\times S_6$ 3C 1A 3C $(7,13,10)(8,14,11)(9,15,12)$
$C_3^2:S_3\times S_6$ 3D $3$ $6$ $C_3^2\times S_6$ 3D 1A 3D $(7,14,10)(8,15,11)(9,13,12)$
$C_3^2:S_3\times S_6$ 3E $3$ $6$ $C_3^2\times S_6$ 3E 1A 3E $(7,15,10)(8,13,11)(9,14,12)$
$C_3^2:S_3\times S_6$ 3F $3$ $40$ $C_3^3:S_3^2$ 3F 1A 3F $(4,6,5)$
$C_3^2:S_3\times S_6$ 3G $3$ $40$ $C_3^3:S_3^2$ 3G 1A 3G $(1,3,5)(2,4,6)$
$C_3^2:S_3\times S_6$ 3H1 $3$ $40$ $C_3^3:S_3^2$ 3H-1 1A 3H-1 $(4,6,5)(7,9,8)(10,12,11)(13,15,14)$
$C_3^2:S_3\times S_6$ 3H-1 $3$ $40$ $C_3^3:S_3^2$ 3H1 1A 3H1 $(4,5,6)(7,8,9)(10,11,12)(13,14,15)$
$C_3^2:S_3\times S_6$ 3I1 $3$ $40$ $C_3^3:S_3^2$ 3I-1 1A 3I-1 $(1,3,5)(2,4,6)(7,9,8)(10,12,11)(13,15,14)$
$C_3^2:S_3\times S_6$ 3I-1 $3$ $40$ $C_3^3:S_3^2$ 3I1 1A 3I1 $(1,5,3)(2,6,4)(7,8,9)(10,11,12)(13,14,15)$
$C_3^2:S_3\times S_6$ 3J $3$ $240$ $S_3\times C_3^3$ 3J 1A 3J $(1,3,5)(2,4,6)(7,10,14)(8,11,15)(9,12,13)$
$C_3^2:S_3\times S_6$ 3K $3$ $240$ $S_3\times C_3^3$ 3K 1A 3K $(1,5,2)(3,6,4)(7,8,9)(13,15,14)$
$C_3^2:S_3\times S_6$ 3L $3$ $240$ $S_3\times C_3^3$ 3L 1A 3L $(2,6,4)(7,13,11)(8,14,12)(9,15,10)$
$C_3^2:S_3\times S_6$ 3M $3$ $240$ $S_3\times C_3^3$ 3M 1A 3M $(1,4,5)(7,15,11)(8,13,12)(9,14,10)$
$C_3^2:S_3\times S_6$ 3N $3$ $240$ $S_3\times C_3^3$ 3N 1A 3N $(1,6,4)(7,12,13)(8,10,14)(9,11,15)$
$C_3^2:S_3\times S_6$ 3O $3$ $240$ $S_3\times C_3^3$ 3O 1A 3O $(1,5,2)(3,6,4)(7,11,14)(8,12,15)(9,10,13)$
$C_3^2:S_3\times S_6$ 3P $3$ $240$ $S_3\times C_3^3$ 3P 1A 3P $(1,5,6)(7,8,9)(10,12,11)$
$C_3^2:S_3\times S_6$ 3Q $3$ $240$ $S_3\times C_3^3$ 3Q 1A 3Q $(1,6,3)(2,4,5)(7,11,15)(8,12,13)(9,10,14)$
$C_3^2:S_3\times S_6$ 4A $4$ $90$ $C_6^2.D_6$ 2D 4A 4A $(3,6,5,4)$
$C_3^2:S_3\times S_6$ 4B $4$ $90$ $C_6^2.D_6$ 2D 4B 4B $(1,2)(3,6,5,4)$
$C_3^2:S_3\times S_6$ 4C $4$ $810$ $C_2^2\times C_{12}$ 2D 4C 4C $(1,4,2,3)(5,6)(7,10)(8,11)(9,12)$
$C_3^2:S_3\times S_6$ 4D $4$ $810$ $C_2^2\times C_{12}$ 2D 4D 4D $(1,3,6,5)(7,11)(8,12)(9,10)$
$C_3^2:S_3\times S_6$ 5A $5$ $144$ $\He_3:C_{10}$ 5A 5A 1A $(1,4,2,6,3)$
$C_3^2:S_3\times S_6$ 6A1 $6$ $9$ $C_6\times S_6$ 3A1 2A 6A-1 $(7,10,9,12,8,11)(13,14,15)$
$C_3^2:S_3\times S_6$ 6A-1 $6$ $9$ $C_6\times S_6$ 3A-1 2A 6A1 $(7,11,8,12,9,10)(13,15,14)$
$C_3^2:S_3\times S_6$ 6B1 $6$ $15$ $C_3^2:D_6\times S_4$ 3A1 2B 6B-1 $(5,6)(7,8,9)(10,11,12)(13,14,15)$
$C_3^2:S_3\times S_6$ 6B-1 $6$ $15$ $C_3^2:D_6\times S_4$ 3A-1 2B 6B1 $(5,6)(7,9,8)(10,12,11)(13,15,14)$
$C_3^2:S_3\times S_6$ 6C1 $6$ $15$ $C_3^2:D_6\times S_4$ 3A1 2C 6C-1 $(1,2)(3,4)(5,6)(7,8,9)(10,11,12)(13,14,15)$
$C_3^2:S_3\times S_6$ 6C-1 $6$ $15$ $C_3^2:D_6\times S_4$ 3A-1 2C 6C1 $(1,2)(3,4)(5,6)(7,9,8)(10,12,11)(13,15,14)$
$C_3^2:S_3\times S_6$ 6D1 $6$ $45$ $C_2\times C_6^2:D_6$ 3A-1 2D 6D-1 $(3,5)(4,6)(7,9,8)(10,12,11)(13,15,14)$
$C_3^2:S_3\times S_6$ 6D-1 $6$ $45$ $C_2\times C_6^2:D_6$ 3A1 2D 6D1 $(3,5)(4,6)(7,8,9)(10,11,12)(13,14,15)$
$C_3^2:S_3\times S_6$ 6E $6$ $90$ $A_4:C_6^2$ 3B 2B 6E $(5,6)(10,11,12)(13,15,14)$
$C_3^2:S_3\times S_6$ 6F $6$ $90$ $A_4:C_6^2$ 3C 2B 6F $(5,6)(7,10,13)(8,11,14)(9,12,15)$
$C_3^2:S_3\times S_6$ 6G $6$ $90$ $A_4:C_6^2$ 3D 2B 6G $(5,6)(7,10,14)(8,11,15)(9,12,13)$
$C_3^2:S_3\times S_6$ 6H $6$ $90$ $A_4:C_6^2$ 3E 2B 6H $(5,6)(7,10,15)(8,11,13)(9,12,14)$
$C_3^2:S_3\times S_6$ 6I $6$ $90$ $A_4:C_6^2$ 3B 2C 6I $(1,2)(3,4)(5,6)(10,11,12)(13,15,14)$
$C_3^2:S_3\times S_6$ 6J $6$ $90$ $A_4:C_6^2$ 3C 2C 6J $(1,2)(3,4)(5,6)(7,10,13)(8,11,14)(9,12,15)$
$C_3^2:S_3\times S_6$ 6K $6$ $90$ $A_4:C_6^2$ 3D 2C 6K $(1,2)(3,4)(5,6)(7,10,14)(8,11,15)(9,12,13)$
$C_3^2:S_3\times S_6$ 6L $6$ $90$ $A_4:C_6^2$ 3E 2C 6L $(1,2)(3,4)(5,6)(7,10,15)(8,11,13)(9,12,14)$
$C_3^2:S_3\times S_6$ 6M $6$ $120$ $C_3^3:D_6$ 3F 2B 6M $(2,3)(4,5,6)$
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