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

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3^5:D_6$ 1A $1$ $1$ $C_3^5:D_6$ 1A 1A $()$
$C_3^5:D_6$ 2A $2$ $9$ $C_3^3:D_6$ 1A 2A $(12,15)(13,14)$
$C_3^5:D_6$ 2B $2$ $27$ $C_3^2\times D_6$ 1A 2B $(2,6)(3,8)(5,9)(10,11)(12,13)(14,15)$
$C_3^5:D_6$ 2C $2$ $27$ $C_3^2\times D_6$ 1A 2C $(2,6)(3,8)(5,9)(10,11)(12,14)(13,15)$
$C_3^5:D_6$ 3A1 $3$ $1$ $C_3^5:D_6$ 3A-1 1A $(1,4,7)(2,5,8)(3,6,9)$
$C_3^5:D_6$ 3A-1 $3$ $1$ $C_3^5:D_6$ 3A1 1A $(1,7,4)(2,8,5)(3,9,6)$
$C_3^5:D_6$ 3B $3$ $2$ $C_3^5:S_3$ 3B 1A $(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3C $3$ $2$ $C_3^5:S_3$ 3C 1A $(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3D1 $3$ $2$ $C_3^5:S_3$ 3D-1 1A $(1,4,7)(2,5,8)(3,6,9)(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3D-1 $3$ $2$ $C_3^5:S_3$ 3D1 1A $(1,7,4)(2,8,5)(3,9,6)(10,14,13)(11,12,15)$
$C_3^5:D_6$ 3E1 $3$ $2$ $C_3^5:S_3$ 3E-1 1A $(1,4,7)(2,5,8)(3,6,9)(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3E-1 $3$ $2$ $C_3^5:S_3$ 3E1 1A $(1,7,4)(2,8,5)(3,9,6)(10,14,13)(11,15,12)$
$C_3^5:D_6$ 3F1 $3$ $3$ $C_3^3:C_6^2$ 3F-1 1A $(3,9,6)$
$C_3^5:D_6$ 3F-1 $3$ $3$ $C_3^3:C_6^2$ 3F1 1A $(3,6,9)$
$C_3^5:D_6$ 3G1 $3$ $3$ $C_3^3:C_6^2$ 3G-1 1A $(2,5,8)(3,6,9)$
$C_3^5:D_6$ 3G-1 $3$ $3$ $C_3^3:C_6^2$ 3G1 1A $(2,8,5)(3,9,6)$
$C_3^5:D_6$ 3H1 $3$ $3$ $C_3^3:C_6^2$ 3H-1 1A $(1,4,7)(2,5,8)(3,9,6)$
$C_3^5:D_6$ 3H-1 $3$ $3$ $C_3^3:C_6^2$ 3H1 1A $(1,7,4)(2,8,5)(3,6,9)$
$C_3^5:D_6$ 3I $3$ $4$ $C_3^5:C_3$ 3I 1A $(11,12,15)$
$C_3^5:D_6$ 3J1 $3$ $4$ $C_3^5:C_3$ 3J-1 1A $(1,4,7)(2,5,8)(3,6,9)(11,12,15)$
$C_3^5:D_6$ 3J-1 $3$ $4$ $C_3^5:C_3$ 3J1 1A $(1,7,4)(2,8,5)(3,9,6)(11,12,15)$
$C_3^5:D_6$ 3K $3$ $6$ $C_3^4:C_6$ 3K 1A $(2,8,5)(3,6,9)$
$C_3^5:D_6$ 3L1 $3$ $6$ $C_3^4:C_6$ 3L-1 1A $(2,5,8)(3,6,9)(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3L-1 $3$ $6$ $C_3^4:C_6$ 3L1 1A $(2,8,5)(3,9,6)(10,14,13)(11,12,15)$
$C_3^5:D_6$ 3M1 $3$ $6$ $C_3^4:C_6$ 3M-1 1A $(2,5,8)(3,6,9)(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3M-1 $3$ $6$ $C_3^4:C_6$ 3M1 1A $(2,8,5)(3,9,6)(10,14,13)(11,15,12)$
$C_3^5:D_6$ 3N1 $3$ $6$ $C_3^4:C_6$ 3N-1 1A $(3,9,6)(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3N-1 $3$ $6$ $C_3^4:C_6$ 3N1 1A $(3,6,9)(10,14,13)(11,12,15)$
$C_3^5:D_6$ 3O1 $3$ $6$ $C_3^4:C_6$ 3O-1 1A $(3,9,6)(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3O-1 $3$ $6$ $C_3^4:C_6$ 3O1 1A $(3,6,9)(10,14,13)(11,15,12)$
$C_3^5:D_6$ 3P1 $3$ $6$ $C_3^4:C_6$ 3P-1 1A $(1,4,7)(2,5,8)(3,9,6)(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3P-1 $3$ $6$ $C_3^4:C_6$ 3P1 1A $(1,7,4)(2,8,5)(3,6,9)(10,14,13)(11,12,15)$
$C_3^5:D_6$ 3Q1 $3$ $6$ $C_3^4:C_6$ 3Q-1 1A $(1,4,7)(2,5,8)(3,9,6)(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3Q-1 $3$ $6$ $C_3^4:C_6$ 3Q1 1A $(1,7,4)(2,8,5)(3,6,9)(10,14,13)(11,15,12)$
$C_3^5:D_6$ 3R $3$ $12$ $C_3^5$ 3R 1A $(2,5,8)(3,9,6)(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3S $3$ $12$ $C_3^5$ 3S 1A $(2,5,8)(3,9,6)(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3T1 $3$ $12$ $C_3^5$ 3T-1 1A $(3,6,9)(11,12,15)$
$C_3^5:D_6$ 3T-1 $3$ $12$ $C_3^5$ 3T1 1A $(3,9,6)(11,12,15)$
$C_3^5:D_6$ 3U1 $3$ $12$ $C_3^5$ 3U-1 1A $(2,5,8)(3,6,9)(11,12,15)$
$C_3^5:D_6$ 3U-1 $3$ $12$ $C_3^5$ 3U1 1A $(2,8,5)(3,9,6)(11,12,15)$
$C_3^5:D_6$ 3V1 $3$ $12$ $C_3^5$ 3V-1 1A $(2,5,8)(3,9,6)(11,12,15)$
$C_3^5:D_6$ 3V-1 $3$ $12$ $C_3^5$ 3V1 1A $(2,5,8)(3,9,6)(10,13,14)$
$C_3^5:D_6$ 3W1 $3$ $12$ $C_3^5$ 3W-1 1A $(1,4,7)(2,5,8)(3,9,6)(11,12,15)$
$C_3^5:D_6$ 3W-1 $3$ $12$ $C_3^5$ 3W1 1A $(1,4,7)(2,8,5)(3,9,6)(11,12,15)$
$C_3^5:D_6$ 3X $3$ $18$ $C_3^2\wr C_2$ 3X 1A $(1,5,3)(2,9,7)(4,8,6)$
$C_3^5:D_6$ 3Y $3$ $36$ $C_3^4$ 3Y 1A $(1,2,3)(4,5,6)(7,8,9)(10,13,14)(11,12,15)$
$C_3^5:D_6$ 3Z $3$ $36$ $C_3^4$ 3Z 1A $(1,2,3)(4,5,6)(7,8,9)(10,13,14)(11,15,12)$
$C_3^5:D_6$ 3AA1 $3$ $36$ $C_3^4$ 3AA-1 1A $(1,2,3)(4,5,6)(7,8,9)(11,12,15)$
$C_3^5:D_6$ 3AA-1 $3$ $36$ $C_3^4$ 3AA1 1A $(1,2,3)(4,5,6)(7,8,9)(10,13,14)$
$C_3^5:D_6$ 6A1 $6$ $9$ $C_3^3:D_6$ 3A1 2A $(1,7,4)(2,8,5)(3,9,6)(10,14)(12,15)$
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