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

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_3^7.D_6$ 1A $1$ $1$ $C_3^7.D_6$ 1A 1A $()$
$C_3^7.D_6$ 2A $2$ $9$ $C_3^5:D_6$ 1A 2A $(1,15)(2,16)(3,4)(5,6)(7,13)(8,10)(9,18)(11,14)(12,17)$
$C_3^7.D_6$ 2B $2$ $243$ not computed 1A 2B $(1,2)(3,9)(4,10)(5,13)(6,17)(7,18)(8,12)(11,15)(14,16)(19,25)(20,26)(21,22)(24,27)$
$C_3^7.D_6$ 2C $2$ $243$ not computed 1A 2C $(1,13)(2,4)(3,16)(7,15)(11,12)(14,17)(20,22)(21,25)(23,24)(26,27)$
$C_3^7.D_6$ 3A1 $3$ $1$ $C_3^7.D_6$ 3A-1 1A $(1,11,16)(2,15,14)(3,13,12)(4,7,17)(5,8,9)(6,10,18)$
$C_3^7.D_6$ 3A-1 $3$ $1$ $C_3^7.D_6$ 3A1 1A $(1,16,11)(2,14,15)(3,12,13)(4,17,7)(5,9,8)(6,18,10)$
$C_3^7.D_6$ 3B $3$ $2$ $C_3^6.C_3.C_6$ 3B 1A $(19,26,27)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3C $3$ $2$ $C_3^5.C_3^3.C_2$ 3C 1A $(1,11,16)(2,14,15)(3,13,12)(4,17,7)(5,9,8)(6,10,18)$
$C_3^7.D_6$ 3D1 $3$ $2$ $C_3^6.C_3.C_6$ 3D-1 1A $(1,11,16)(2,15,14)(3,13,12)(4,7,17)(5,8,9)(6,10,18)(19,27,26)(20,24,25)(21,23,22)$
$C_3^7.D_6$ 3D-1 $3$ $2$ $C_3^6.C_3.C_6$ 3D1 1A $(1,16,11)(2,14,15)(3,12,13)(4,17,7)(5,9,8)(6,18,10)(19,26,27)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3E1 $3$ $2$ $C_3^5.C_3^3.C_2$ 3E-1 1A $(1,16,11)(3,12,13)(6,18,10)$
$C_3^7.D_6$ 3E-1 $3$ $2$ $C_3^5.C_3^3.C_2$ 3E1 1A $(1,11,16)(3,13,12)(6,10,18)$
$C_3^7.D_6$ 3F1 $3$ $3$ $C_3^7.C_2^2$ 3F-1 1A $(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3F-1 $3$ $3$ $C_3^7.C_2^2$ 3F1 1A $(20,24,25)(21,22,23)$
$C_3^7.D_6$ 3G1 $3$ $3$ $C_3^7.C_2^2$ 3G-1 1A $(1,11,16)(2,15,14)(3,13,12)(4,7,17)(5,8,9)(6,10,18)(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3G-1 $3$ $3$ $C_3^7.C_2^2$ 3G1 1A $(1,16,11)(2,14,15)(3,12,13)(4,17,7)(5,9,8)(6,18,10)(20,24,25)(21,22,23)$
$C_3^7.D_6$ 3H1 $3$ $3$ $C_3^7.C_2^2$ 3H-1 1A $(1,11,16)(2,15,14)(3,13,12)(4,7,17)(5,8,9)(6,10,18)(20,24,25)(21,22,23)$
$C_3^7.D_6$ 3H-1 $3$ $3$ $C_3^7.C_2^2$ 3H1 1A $(1,16,11)(2,14,15)(3,12,13)(4,17,7)(5,9,8)(6,18,10)(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3I $3$ $4$ $C_3^7.C_3$ 3I 1A $(1,11,16)(2,14,15)(3,13,12)(4,17,7)(5,9,8)(6,10,18)(19,26,27)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3J1 $3$ $4$ $C_3^7.C_3$ 3J-1 1A $(2,14,15)(4,17,7)(5,9,8)(19,26,27)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3J-1 $3$ $4$ $C_3^7.C_3$ 3J1 1A $(2,15,14)(4,7,17)(5,8,9)(19,26,27)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3K $3$ $6$ $C_3^7.C_2$ 3K 1A $(21,23,22)$
$C_3^7.D_6$ 3L $3$ $6$ $C_3^7.C_2$ 3L 1A $(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3M $3$ $6$ $C_3^7.C_2$ 3M 1A $(19,27,26)(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3N $3$ $6$ $C_3^7.C_2$ 3N 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)$
$C_3^7.D_6$ 3O $3$ $6$ $C_3^7.C_2$ 3O 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(20,25,24)$
$C_3^7.D_6$ 3P $3$ $6$ $C_3^7.C_2$ 3P 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(20,24,25)$
$C_3^7.D_6$ 3Q $3$ $6$ $C_3^7.C_2$ 3Q 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,27,26)(21,23,22)$
$C_3^7.D_6$ 3R $3$ $6$ $C_3^7.C_2$ 3R 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,27,26)(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3S $3$ $6$ $C_3^7.C_2$ 3S 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,27,26)(20,24,25)(21,23,22)$
$C_3^7.D_6$ 3T $3$ $6$ $C_3^7.C_2$ 3T 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,26,27)(21,22,23)$
$C_3^7.D_6$ 3U $3$ $6$ $C_3^7.C_2$ 3U 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,26,27)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3V $3$ $6$ $C_3^7.C_2$ 3V 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,26,27)(20,24,25)(21,22,23)$
$C_3^7.D_6$ 3W $3$ $6$ $C_3^7.C_2$ 3W 1A $(1,18,12)(2,7,8)(3,11,6)(4,5,14)(9,15,17)(10,13,16)$
$C_3^7.D_6$ 3X1 $3$ $6$ $C_3^7.C_2$ 3X-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(21,23,22)$
$C_3^7.D_6$ 3X-1 $3$ $6$ $C_3^7.C_2$ 3X1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(21,22,23)$
$C_3^7.D_6$ 3Y1 $3$ $6$ $C_3^7.C_2$ 3Y-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(21,22,23)$
$C_3^7.D_6$ 3Y-1 $3$ $6$ $C_3^7.C_2$ 3Y1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(21,23,22)$
$C_3^7.D_6$ 3Z1 $3$ $6$ $C_3^7.C_2$ 3Z-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3Z-1 $3$ $6$ $C_3^7.C_2$ 3Z1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(20,24,25)(21,22,23)$
$C_3^7.D_6$ 3AA1 $3$ $6$ $C_3^7.C_2$ 3AA-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3AA-1 $3$ $6$ $C_3^7.C_2$ 3AA1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(20,24,25)(21,23,22)$
$C_3^7.D_6$ 3AB1 $3$ $6$ $C_3^7.C_2$ 3AB-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(20,24,25)(21,23,22)$
$C_3^7.D_6$ 3AB-1 $3$ $6$ $C_3^7.C_2$ 3AB1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3AC1 $3$ $6$ $C_3^7.C_2$ 3AC-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(20,24,25)(21,22,23)$
$C_3^7.D_6$ 3AC-1 $3$ $6$ $C_3^7.C_2$ 3AC1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(20,25,24)(21,23,22)$
$C_3^7.D_6$ 3AD1 $3$ $6$ $C_3^7.C_2$ 3AD-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,27,26)(21,22,23)$
$C_3^7.D_6$ 3AD-1 $3$ $6$ $C_3^7.C_2$ 3AD1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(19,26,27)(21,23,22)$
$C_3^7.D_6$ 3AE1 $3$ $6$ $C_3^7.C_2$ 3AE-1 1A $(1,3,10)(2,17,5)(4,8,15)(6,16,12)(7,9,14)(11,13,18)(19,27,26)(20,25,24)(21,22,23)$
$C_3^7.D_6$ 3AE-1 $3$ $6$ $C_3^7.C_2$ 3AE1 1A $(1,10,3)(2,5,17)(4,15,8)(6,12,16)(7,14,9)(11,18,13)(19,26,27)(20,24,25)(21,23,22)$
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