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Results (48 matches)
Download displayed columns for resultsElements of the group are displayed as permutations of degree 27.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^6.(S_3\times Q_8)$ | 1A | $1$ | $1$ | $C_3^6.(S_3\times Q_8)$ | 1A | 1A | $()$ |
| $C_3^6.(S_3\times Q_8)$ | 2A | $2$ | $27$ | $C_2\times C_3^4:Q_8$ | 1A | 2A | $(10,22)(11,21)(12,20)(13,19)(14,27)(15,26)(16,25)(17,24)(18,23)$ |
| $C_3^6.(S_3\times Q_8)$ | 2B | $2$ | $243$ | $C_2\times \PSU(3,2)$ | 1A | 2B | $(1,20)(2,19)(3,24)(4,26)(5,25)(6,21)(7,23)(8,22)(9,27)(10,18)(12,16)(13,15)(14,17)$ |
| $C_3^6.(S_3\times Q_8)$ | 2C | $2$ | $729$ | $S_3\times Q_8$ | 1A | 2C | $(1,9)(3,7)(4,6)(5,8)(10,14)(11,13)(12,18)(16,17)(19,22)(20,21)(23,27)(24,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 3A | $3$ | $8$ | $C_3^4.C_3^3.C_2$ | 3A | 1A | $(1,8,3)(2,6,4)(5,9,7)(10,12,17)(11,13,15)(14,16,18)(19,26,21)(20,24,22)(23,27,25)$ |
| $C_3^6.(S_3\times Q_8)$ | 3B | $3$ | $24$ | $C_3^5:C_6$ | 3B | 1A | $(10,13,16)(11,14,17)(12,15,18)(19,25,22)(20,26,23)(21,27,24)$ |
| $C_3^6.(S_3\times Q_8)$ | 3C | $3$ | $24$ | $C_3^5:C_6$ | 3C | 1A | $(1,6,5)(2,7,3)(4,9,8)$ |
| $C_3^6.(S_3\times Q_8)$ | 3D | $3$ | $24$ | $C_3^5:C_6$ | 3D | 1A | $(1,3,8)(2,4,6)(5,7,9)(19,26,21)(20,24,22)(23,27,25)$ |
| $C_3^6.(S_3\times Q_8)$ | 3E | $3$ | $24$ | $C_3^5:C_6$ | 3E | 1A | $(1,8,3)(2,6,4)(5,9,7)(10,16,13)(11,17,14)(12,18,15)(19,22,25)(20,23,26)(21,24,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3F | $3$ | $24$ | $C_3^5:C_6$ | 3F | 1A | $(1,8,3)(2,6,4)(5,9,7)(10,15,14)(11,16,12)(13,18,17)(19,23,24)(20,21,25)(22,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3G | $3$ | $24$ | $C_3^5:C_6$ | 3G | 1A | $(1,3,8)(2,4,6)(5,7,9)(10,18,11)(12,14,13)(15,17,16)(19,20,27)(21,22,23)(24,25,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 3H | $3$ | $24$ | $C_3^5:C_6$ | 3H | 1A | $(1,5,6)(2,3,7)(4,8,9)(10,15,14)(11,16,12)(13,18,17)(19,24,23)(20,25,21)(22,27,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 3I | $3$ | $24$ | $C_3^5:C_6$ | 3I | 1A | $(1,5,6)(2,3,7)(4,8,9)(10,18,11)(12,14,13)(15,17,16)(19,20,27)(21,22,23)(24,25,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 3J | $3$ | $24$ | $C_3^5:C_6$ | 3J | 1A | $(1,3,8)(2,4,6)(5,7,9)(10,15,14)(11,16,12)(13,18,17)(19,23,24)(20,21,25)(22,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3K | $3$ | $24$ | $C_3^5:C_6$ | 3K | 1A | $(1,3,8)(2,4,6)(5,7,9)(10,11,18)(12,13,14)(15,16,17)(19,27,20)(21,23,22)(24,26,25)$ |
| $C_3^6.(S_3\times Q_8)$ | 3L | $3$ | $48$ | $C_3^6$ | 3L | 1A | $(10,11,18)(12,13,14)(15,16,17)(19,21,26)(20,22,24)(23,25,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3M | $3$ | $48$ | $C_3^6$ | 3M | 1A | $(10,11,18)(12,13,14)(15,16,17)(19,22,25)(20,23,26)(21,24,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3N | $3$ | $48$ | $C_3^6$ | 3N | 1A | $(10,11,18)(12,13,14)(15,16,17)(19,23,24)(20,21,25)(22,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3O | $3$ | $48$ | $C_3^6$ | 3O | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,11,18)(12,13,14)(15,16,17)(19,21,26)(20,22,24)(23,25,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3P | $3$ | $48$ | $C_3^6$ | 3P | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,11,18)(12,13,14)(15,16,17)(19,22,25)(20,23,26)(21,24,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3Q | $3$ | $48$ | $C_3^6$ | 3Q | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,11,18)(12,13,14)(15,16,17)(19,23,24)(20,21,25)(22,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3R | $3$ | $48$ | $C_3^6$ | 3R | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,12,17)(11,13,15)(14,16,18)(19,22,25)(20,23,26)(21,24,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3S | $3$ | $48$ | $C_3^6$ | 3S | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,12,17)(11,13,15)(14,16,18)(19,23,24)(20,21,25)(22,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 3T | $3$ | $48$ | $C_3^6$ | 3T | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,12,17)(11,13,15)(14,16,18)(19,24,23)(20,25,21)(22,27,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 3U | $3$ | $48$ | $C_3^6$ | 3U | 1A | $(1,2,9)(3,4,5)(6,7,8)(10,12,17)(11,13,15)(14,16,18)(19,25,22)(20,26,23)(21,27,24)$ |
| $C_3^6.(S_3\times Q_8)$ | 3V | $3$ | $162$ | $C_3^3:Q_8$ | 3V | 1A | $(1,24,16)(2,25,15)(3,20,14)(4,27,13)(5,19,12)(6,23,11)(7,21,10)(8,22,18)(9,26,17)$ |
| $C_3^6.(S_3\times Q_8)$ | 4A | $4$ | $1458$ | $C_4\times S_3$ | 2C | 4A | $(1,6,9,4)(3,8,7,5)(10,12,14,18)(11,17,13,16)(19,20,22,21)(23,26,27,24)$ |
| $C_3^6.(S_3\times Q_8)$ | 4B | $4$ | $1458$ | $C_4\times S_3$ | 2C | 4B | $(1,3,6,4)(2,7,8,9)(10,15,16,11)(12,18,14,17)(19,23,22,27)(20,24,21,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 4C | $4$ | $1458$ | $C_4\times S_3$ | 2C | 4C | $(2,7,9,4)(3,5,8,6)(10,17,13,15)(11,14,12,18)(19,23,27,26)(21,24,25,22)$ |
| $C_3^6.(S_3\times Q_8)$ | 4D | $4$ | $4374$ | $C_2\times C_4$ | 2C | 4D | $(1,15,6,17)(2,14,8,18)(3,12,4,11)(5,16)(7,13,9,10)(19,21,24,22)(20,25,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 4E | $4$ | $4374$ | $C_2\times C_4$ | 2C | 4E | $(1,13,8,12)(2,11,7,17)(3,14)(4,18,5,16)(6,10,9,15)(19,27,25,26)(20,23,24,21)$ |
| $C_3^6.(S_3\times Q_8)$ | 4F | $4$ | $4374$ | $C_2\times C_4$ | 2C | 4F | $(1,17,3,18)(2,14,5,12)(4,15,9,11)(6,10,7,16)(8,13)(19,23,25,21)(20,26,24,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 6A | $6$ | $216$ | $C_3^3\times C_6$ | 3B | 2A | $(10,25,13,22,16,19)(11,24,14,21,17,27)(12,23,15,20,18,26)$ |
| $C_3^6.(S_3\times Q_8)$ | 6B | $6$ | $216$ | $C_3^3\times C_6$ | 3C | 2A | $(1,5,6)(2,3,7)(4,8,9)(10,19)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)$ |
| $C_3^6.(S_3\times Q_8)$ | 6C | $6$ | $216$ | $C_3^3\times C_6$ | 3A | 2A | $(1,10,3,17,8,12)(2,18,4,16,6,14)(5,15,7,13,9,11)(19,26,21)(20,24,22)(23,27,25)$ |
| $C_3^6.(S_3\times Q_8)$ | 6D | $6$ | $216$ | $C_3^3\times C_6$ | 3E | 2A | $(1,3,8)(2,4,6)(5,7,9)(10,23,16,26,13,20)(11,22,17,25,14,19)(12,27,18,21,15,24)$ |
| $C_3^6.(S_3\times Q_8)$ | 6E | $6$ | $216$ | $C_3^3\times C_6$ | 3F | 2A | $(1,3,8)(2,4,6)(5,7,9)(10,20,15,21,14,25)(11,19,16,23,12,24)(13,26,18,27,17,22)$ |
| $C_3^6.(S_3\times Q_8)$ | 6F | $6$ | $216$ | $C_3^3\times C_6$ | 3G | 2A | $(1,8,3)(2,6,4)(5,9,7)(10,20,18,27,11,19)(12,24,14,25,13,26)(15,21,17,22,16,23)$ |
| $C_3^6.(S_3\times Q_8)$ | 6G | $6$ | $216$ | $C_3^3\times C_6$ | 3H | 2A | $(1,18,5,17,6,13)(2,11,3,16,7,12)(4,15,8,14,9,10)(19,23,24)(20,21,25)(22,26,27)$ |
| $C_3^6.(S_3\times Q_8)$ | 6H | $6$ | $216$ | $C_3^3\times C_6$ | 3I | 2A | $(1,6,5)(2,7,3)(4,9,8)(10,22,18,23,11,21)(12,20,14,27,13,19)(15,26,17,24,16,25)$ |
| $C_3^6.(S_3\times Q_8)$ | 6I | $6$ | $216$ | $C_3^3\times C_6$ | 3J | 2A | $(1,8,3)(2,6,4)(5,9,7)(10,27,15,22,14,26)(11,20,16,21,12,25)(13,24,18,19,17,23)$ |
| $C_3^6.(S_3\times Q_8)$ | 6J | $6$ | $216$ | $C_3^3\times C_6$ | 3K | 2A | $(1,8,3)(2,6,4)(5,9,7)(10,27,11,20,18,19)(12,25,13,24,14,26)(15,22,16,21,17,23)$ |
| $C_3^6.(S_3\times Q_8)$ | 6K | $6$ | $1458$ | $C_3\times Q_8$ | 3V | 2C | $(1,17,24,9,16,26)(2,15,25)(3,10,20,7,14,21)(4,11,27,6,13,23)(5,18,19,8,12,22)$ |
| $C_3^6.(S_3\times Q_8)$ | 6L | $6$ | $1944$ | $C_3\times C_6$ | 3D | 2B | $(1,22,3,20,8,24)(2,21,4,19,6,26)(5,27,7,25,9,23)(10,18)(12,16)(13,15)(14,17)$ |
| $C_3^6.(S_3\times Q_8)$ | 9A | $9$ | $1296$ | $C_3\times C_9$ | 9A | 3A | $(1,23,15,8,27,11,3,25,13)(2,21,17,6,19,10,4,26,12)(5,24,14,9,22,16,7,20,18)$ |
| $C_3^6.(S_3\times Q_8)$ | 12A | $12$ | $2916$ | $C_{12}$ | 6K | 4A | $(1,27,17,6,24,13,9,23,16,4,26,11)(2,25,15)(3,19,10,8,20,12,7,22,14,5,21,18)$ |
| $C_3^6.(S_3\times Q_8)$ | 12B | $12$ | $2916$ | $C_{12}$ | 6K | 4B | $(1,24,18,3,21,14,6,26,17,4,20,12)(2,23,10,7,22,15,8,27,16,9,19,11)(5,25,13)$ |
| $C_3^6.(S_3\times Q_8)$ | 12C | $12$ | $2916$ | $C_{12}$ | 6K | 4C | $(1,16,20)(2,13,19,7,15,23,9,10,27,4,17,26)(3,11,24,5,14,25,8,12,22,6,18,21)$ |