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Results (41 matches)

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Elements of the group are displayed as permutations of degree 27.

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3^3:S_3^2.S_4$ 1A $1$ $1$ $C_3^3:S_3^2.S_4$ 1A 1A $()$
$C_3^3:S_3^2.S_4$ 2A $2$ $27$ $C_2\times C_3^2:\GL(2,3)$ 1A 2A $(1,16)(2,18)(3,17)(4,13)(5,15)(6,14)(7,10)(8,12)(9,11)(19,25)(20,27)(21,26)(23,24)$
$C_3^3:S_3^2.S_4$ 2B $2$ $27$ $C_2\times C_3^2:\GL(2,3)$ 1A 2B $(2,3)(4,6)(7,8)(10,12)(13,14)(17,18)(19,20)(23,24)(25,27)$
$C_3^3:S_3^2.S_4$ 2C $2$ $81$ $S_3\times \GL(2,3)$ 1A 2C $(1,11)(2,12)(3,10)(4,17)(5,18)(6,16)(7,14)(8,15)(9,13)(22,25)(23,26)(24,27)$
$C_3^3:S_3^2.S_4$ 2D $2$ $108$ $C_6.S_3^2$ 1A 2D $(4,23)(5,24)(6,22)(7,18)(8,16)(9,17)(10,21)(11,19)(12,20)$
$C_3^3:S_3^2.S_4$ 2E $2$ $324$ $S_3\times D_6$ 1A 2E $(1,9)(2,8)(3,7)(4,6)(10,16)(11,18)(12,17)(14,15)(19,26)(20,25)(21,27)(22,23)$
$C_3^3:S_3^2.S_4$ 3A $3$ $2$ $C_3^3:C_3^2:\GL(2,3)$ 3A 1A $(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27)$
$C_3^3:S_3^2.S_4$ 3B $3$ $24$ $C_3^3:S_3^2$ 3B 1A $(1,12,20)(2,10,21)(3,11,19)(4,15,23)(5,13,24)(6,14,22)(7,18,26)(8,16,27)(9,17,25)$
$C_3^3:S_3^2.S_4$ 3C $3$ $24$ $C_3^3:S_3^2$ 3C 1A $(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)$
$C_3^3:S_3^2.S_4$ 3D $3$ $48$ $C_3^4:S_3$ 3D 1A $(1,22,16)(2,23,17)(3,24,18)(4,27,11)(5,25,12)(6,26,10)(7,20,15)(8,21,13)(9,19,14)$
$C_3^3:S_3^2.S_4$ 3E $3$ $72$ $C_3\wr C_2^2$ 3E 1A $(1,17,24)(2,18,22)(3,16,23)(4,27,11)(5,25,12)(6,26,10)$
$C_3^3:S_3^2.S_4$ 3F $3$ $144$ $C_3^2\wr C_2$ 3F 1A $(1,5,9)(2,6,7)(3,4,8)(10,17,15)(11,18,13)(12,16,14)(19,20,21)(22,23,24)(25,26,27)$
$C_3^3:S_3^2.S_4$ 3G $3$ $144$ $C_3^3:S_3$ 3G 1A $(1,11,19)(2,12,20)(3,10,21)(4,14,22)(5,15,23)(6,13,24)(7,17,25)(8,18,26)(9,16,27)$
$C_3^3:S_3^2.S_4$ 3H $3$ $432$ $S_3\times C_3^2$ 3H 1A $(1,13,26)(2,14,27)(3,15,25)(4,21,16)(5,19,17)(6,20,18)(7,8,9)(10,12,11)$
$C_3^3:S_3^2.S_4$ 3I $3$ $432$ $S_3\times C_3^2$ 3I 1A $(1,25,12)(2,26,10)(3,27,11)(4,19,15)(5,20,13)(6,21,14)(7,22,18)(8,23,16)(9,24,17)$
$C_3^3:S_3^2.S_4$ 4A $4$ $486$ $S_3\times C_8$ 2C 4A $(1,15,19,17)(2,13,20,18)(3,14,21,16)(4,22,27,9)(5,23,25,7)(6,24,26,8)$
$C_3^3:S_3^2.S_4$ 4B $4$ $1458$ $C_2\times C_8$ 2C 4B $(1,19,7,18)(2,21,8,17)(3,20,9,16)(4,5)(10,13,26,23)(11,15,27,22)(12,14,25,24)$
$C_3^3:S_3^2.S_4$ 6A $6$ $162$ $C_3\times \GL(2,3)$ 3A 2C $(1,21,2,19,3,20)(4,26,5,27,6,25)(7,22,8,23,9,24)(10,12,11)(13,17,14,18,15,16)$
$C_3^3:S_3^2.S_4$ 6B $6$ $216$ $C_3^2:D_6$ 3A 2D $(1,25,2,26,3,27)(4,19,5,20,6,21)(7,22,8,23,9,24)(10,12,11)(13,15,14)(16,18,17)$
$C_3^3:S_3^2.S_4$ 6C $6$ $216$ $C_3^2:D_6$ 3C 2A $(1,19,2,21,3,20)(4,26,6,27,5,25)(7,24)(8,23)(9,22)(10,12)(13,16,14,18,15,17)$
$C_3^3:S_3^2.S_4$ 6D $6$ $216$ $C_3^2:D_6$ 3B 2B $(1,16,23,2,18,24)(3,17,22)(4,10,26,5,12,27)(6,11,25)(7,13,20,8,15,21)(9,14,19)$
$C_3^3:S_3^2.S_4$ 6E $6$ $648$ $C_6\times S_3$ 3B 2E $(1,25,12,9,20,17)(2,27,10,8,21,16)(3,26,11,7,19,18)(4,22,15,6,23,14)(5,24,13)$
$C_3^3:S_3^2.S_4$ 6F $6$ $648$ $C_6\times S_3$ 3B 2D $(1,13,25)(2,14,26)(3,15,27)(4,8,19,23,16,11)(5,9,20,24,17,12)(6,7,21,22,18,10)$
$C_3^3:S_3^2.S_4$ 6G $6$ $648$ $C_6\times S_3$ 3E 2A $(1,25,17,12,24,5)(2,27,18,11,22,4)(3,26,16,10,23,6)(7,15)(8,14)(9,13)(19,21)$
$C_3^3:S_3^2.S_4$ 6H $6$ $648$ $C_6\times S_3$ 3E 2B $(1,16,22)(2,18,23,3,17,24)(4,27,10,6,25,12)(5,26,11)(7,8)(13,14)(19,20)$
$C_3^3:S_3^2.S_4$ 6I $6$ $648$ $C_6\times S_3$ 3C 2D $(1,9)(2,7)(3,8)(10,11,12)(13,18,15,17,14,16)(19,22,20,23,21,24)(25,27,26)$
$C_3^3:S_3^2.S_4$ 6J $6$ $648$ $C_6\times S_3$ 3C 2E $(1,8,3,9,2,7)(4,6)(10,13,11,15,12,14)(16,18)(19,21)(22,25,23,27,24,26)$
$C_3^3:S_3^2.S_4$ 6K $6$ $648$ $C_6\times S_3$ 3E 2C $(1,25,24,5,17,12)(2,26,22,6,18,10)(3,27,23,4,16,11)(13,20)(14,21)(15,19)$
$C_3^3:S_3^2.S_4$ 6L $6$ $1296$ $C_3\times C_6$ 3F 2C $(1,13,5,11,9,18)(2,14,6,12,7,16)(3,15,4,10,8,17)(19,21,20)(22,27,23,25,24,26)$
$C_3^3:S_3^2.S_4$ 6M $6$ $1296$ $C_3\times C_6$ 3H 2A $(1,21,13,16,26,4)(2,20,14,18,27,6)(3,19,15,17,25,5)(7,11,8,10,9,12)(23,24)$
$C_3^3:S_3^2.S_4$ 6N $6$ $1296$ $C_3\times C_6$ 3G 2D $(1,27,11,9,19,16)(2,25,12,7,20,17)(3,26,10,8,21,18)(4,22,14)(5,23,15)(6,24,13)$
$C_3^3:S_3^2.S_4$ 6O $6$ $1296$ $C_3\times C_6$ 3D 2E $(1,9,22,19,16,14)(2,8,23,21,17,13)(3,7,24,20,18,15)(4,12,27,5,11,25)(6,10,26)$
$C_3^3:S_3^2.S_4$ 6P $6$ $1296$ $C_3\times C_6$ 3I 2B $(1,11,25,3,12,27)(2,10,26)(4,13,19,5,15,20)(6,14,21)(7,18,22)(8,17,23,9,16,24)$
$C_3^3:S_3^2.S_4$ 8A1 $8$ $486$ $S_3\times C_8$ 4A 8A1 $(1,8,15,6,19,24,17,26)(2,9,13,4,20,22,18,27)(3,7,14,5,21,23,16,25)$
$C_3^3:S_3^2.S_4$ 8A-1 $8$ $486$ $S_3\times C_8$ 4A 8A-1 $(1,26,17,24,19,6,15,8)(2,27,18,22,20,4,13,9)(3,25,16,23,21,5,14,7)$
$C_3^3:S_3^2.S_4$ 8B1 $8$ $1458$ $C_2\times C_8$ 4A 8B1 $(1,13,19,27,8,22,17,11)(2,15,20,26,9,24,18,10)(3,14,21,25,7,23,16,12)(4,6)$
$C_3^3:S_3^2.S_4$ 8B-1 $8$ $1458$ $C_2\times C_8$ 4A 8B-1 $(1,11,17,22,8,27,19,13)(2,10,18,24,9,26,20,15)(3,12,16,23,7,25,21,14)(4,6)$
$C_3^3:S_3^2.S_4$ 9A $9$ $864$ $C_3\times C_9$ 9A 3A $(1,5,24,3,4,23,2,6,22)(7,14,16,9,13,18,8,15,17)(10,27,21,12,26,20,11,25,19)$
$C_3^3:S_3^2.S_4$ 12A $12$ $972$ $C_{24}$ 6A 4A $(1,18,21,15,2,16,19,13,3,17,20,14)(4,7,26,22,5,8,27,23,6,9,25,24)(10,11,12)$
$C_3^3:S_3^2.S_4$ 24A1 $24$ $972$ $C_{24}$ 12A 8A1 $(1,5,18,8,21,27,15,23,2,6,16,9,19,25,13,24,3,4,17,7,20,26,14,22)(10,12,11)$
$C_3^3:S_3^2.S_4$ 24A-1 $24$ $972$ $C_{24}$ 12A 8A-1 $(1,22,14,26,20,7,17,4,3,24,13,25,19,9,16,6,2,23,15,27,21,8,18,5)(10,11,12)$
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