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Results (33 matches)
Download displayed columns for resultsElements of the group are displayed as permutations of degree 81.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | ||||||
| $C_3^3:S_3.C_2^4:S_5$ | 1A | $1$ | $1$ | $C_3^3:S_3.C_2^4:S_5$ | 1A | 1A | 1A | $()$ |
| $C_3^3:S_3.C_2^4:S_5$ | 2A | $2$ | $81$ | $C_2.C_2^4:S_5$ | 1A | 2A | 2A | $(1,2)(3,49)(4,53)(5,32)(6,12)(7,38)(9,19)(10,24)(11,25)(13,28)(14,78)(15,34)(16,40)(17,18)(20,62)(21,30)(22,47)(23,37)(26,70)(27,33)(29,65)(31,55)(35,39)(36,57)(41,54)(42,48)(43,46)(44,56)(45,63)(50,64)(51,68)(52,67)(58,69)(59,80)(60,73)(61,71)(66,72)(74,79)(75,81)(76,77)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 2B | $2$ | $90$ | $C_3^2.Q_8^2.S_3$ | 1A | 2B | 2B | $(2,8)(3,39)(6,27)(7,12)(9,58)(10,43)(11,44)(13,18)(14,77)(15,19)(16,80)(17,55)(20,57)(21,65)(22,63)(23,64)(29,68)(30,59)(32,56)(33,38)(34,42)(35,48)(36,75)(37,81)(40,54)(41,51)(45,61)(46,53)(47,78)(49,69)(50,72)(52,71)(60,70)(62,66)(67,76)(73,74)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 2C | $2$ | $1080$ | $F_9:C_2^2$ | 1A | 2C | 2C | $(1,23)(2,62)(3,28)(4,14)(5,15)(6,36)(7,79)(8,60)(9,76)(10,71)(11,49)(12,64)(13,29)(16,53)(17,56)(18,43)(20,26)(22,68)(24,65)(25,61)(27,66)(30,63)(31,40)(32,78)(33,75)(34,55)(37,74)(38,70)(39,45)(42,67)(47,58)(48,69)(51,80)(52,59)(54,77)(72,81)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 3A | $3$ | $80$ | $C_3^2.Q_8:\He_3.C_2$ | 3A | 1A | 3A | $(1,80,29)(2,65,59)(3,22,74)(4,33,16)(5,66,78)(6,21,43)(7,51,10)(8,41,54)(9,77,73)(11,23,67)(12,46,30)(13,20,58)(14,72,32)(15,75,55)(17,35,64)(18,50,39)(19,60,76)(24,68,38)(25,52,37)(26,42,71)(27,53,40)(28,69,62)(31,81,34)(36,45,44)(47,49,79)(48,70,61)(56,63,57)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 3B | $3$ | $720$ | $F_9:C_6$ | 3B | 1A | 3B | $(1,38,33)(2,7,27)(3,75,10)(4,34,66)(5,37,80)(9,36,30)(11,20,51)(13,14,22)(15,72,53)(16,69,26)(19,57,21)(23,59,32)(24,49,81)(25,62,68)(28,78,47)(29,42,79)(31,71,52)(35,50,41)(39,64,54)(40,58,70)(43,56,60)(44,73,46)(48,74,65)(55,61,67)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 3C | $3$ | $5760$ | $S_3\times C_3^2$ | 3C | 1A | 3C | $(1,26,31)(2,50,71)(3,61,23)(4,24,5)(6,37,13)(7,20,14)(8,72,52)(9,78,70)(10,41,49)(11,30,16)(12,57,77)(15,40,65)(17,75,42)(18,27,81)(19,54,21)(22,33,73)(25,28,79)(29,53,35)(32,76,62)(34,55,36)(38,74,63)(39,45,64)(43,51,69)(44,59,80)(46,48,68)(47,60,58)(56,67,66)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 4A | $4$ | $540$ | $\PSU(3,2):C_8$ | 2B | 4A | 4A | $(2,57,28,9)(3,36,19,72)(4,20,38,35)(5,53,7,47)(6,46,26,52)(8,23,31,48)(10,79,78,27)(11,34,61,54)(12,71,25,43)(13,68,17,16)(14,74,44,76)(21,30,42,37)(22,45,60,32)(24,64,33,58)(40,51,49,66)(41,67,81,70)(56,69,77,65)(59,63,62,73)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 4B | $4$ | $1620$ | $\GL(2,3):C_4$ | 2A | 4B | 4B | $(1,75,80,39)(2,23,41,56)(3,6,60,53)(4,59,68,54)(5,72,52,45)(7,36,46,32)(8,70,65,9)(10,40,30,43)(11,20,63,17)(12,79,51,42)(13,61,35,73)(14,76,44,74)(15,50,18,55)(16,34,38,62)(19,26,22,47)(21,25,27,66)(24,58,33,64)(28,48,81,77)(31,67,69,57)(37,71,78,49)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 4C | $4$ | $3240$ | $\GL(2,3):C_2$ | 2A | 4C | 4C | $(1,4,2,53)(3,56,49,44)(5,50,32,64)(6,76,12,77)(7,15,38,34)(9,26,19,70)(10,43,24,46)(11,52,25,67)(13,48,28,42)(14,74,78,79)(16,57,40,36)(17,63,18,45)(20,31,62,55)(21,58,30,69)(22,65,47,29)(23,54,37,41)(27,72,33,66)(35,59,39,80)(51,71,68,61)(60,81,73,75)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 4D | $4$ | $4860$ | $Q_8:C_8$ | 2B | 4D | 4D | $(1,19,68,72)(2,42,66,8)(3,13,17,36)(4,33)(5,41,59,71)(6,50,52,77)(7,67,47,15)(9,21,18,37)(10,11,79,75)(12,62,81,53)(14,80,76,38)(20,64,45,74)(22,58,35,44)(23,49,55,51)(24,32,29,60)(25,73,43,39)(26,78,54,65)(27,46,69,34)(28,31,40,30)(48,57)(56,61)(63,70)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 4E | $4$ | $9720$ | $C_4\wr C_2$ | 2A | 4E | 4E | $(1,28,33,52)(2,21,6,59)(3,7,44,8)(4,39,80,48)(5,72,42,64)(9,26,11,66)(10,61,41,18)(12,70,27,50)(13,35,76,32)(14,57,17,75)(15,34,56,49)(16,74,29,36)(19,77,58,67)(20,79,60,81)(22,46,45,40)(23,55,73,63)(24,65,68,43)(25,30,69,53)(31,71,47,78)(37,51,62,54)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 5A | $5$ | $31104$ | $C_{10}$ | 5A | 5A | 1A | $(1,16,27,64,45)(2,8,40,53,52)(3,60,46,39,59)(4,35,10,67,51)(5,28,77,56,13)(6,22,71,20,58)(7,50,26,43,79)(9,15,12,11,36)(14,68,54,37,19)(17,81,63,21,41)(18,76,62,70,29)(23,31,75,69,80)(24,74,65,49,34)(25,42,78,30,33)(32,57,66,72,55)(38,47,44,48,73)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 6A | $6$ | $720$ | $C_3^2:\GL(2,3)$ | 3A | 2B | 6A | $(1,29,80)(2,62,65,28,59,69)(3,76,22,19,74,60)(4,68,33,38,16,24)(5,10,66,7,78,51)(6,71,21,26,43,42)(8,34,41,31,54,81)(9,63,77,57,73,56)(11,70,23,61,67,48)(12,37,46,25,30,52)(13,64,20,17,58,35)(14,45,72,44,32,36)(15,55,75)(18,39,50)(27,49,53,79,40,47)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 6B | $6$ | $6480$ | $C_3\times \SD_{16}$ | 3B | 2A | 6B | $(1,27,38,2,33,7)(3,24,75,49,10,81)(4,72,34,53,66,15)(5,59,37,32,80,23)(6,12)(9,21,36,19,30,57)(11,68,20,25,51,62)(13,47,14,28,22,78)(16,70,69,40,26,58)(17,18)(29,74,42,65,79,48)(31,67,71,55,52,61)(35,54,50,39,41,64)(43,73,56,46,60,44)(45,63)(76,77)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 6C | $6$ | $8640$ | $C_6\times S_3$ | 3B | 2B | 6C | $(1,18,78,6,52,45)(2,14,55,7,13,61)(3,10,23,32,40,70)(4,60,34,30,66,39)(5,44,49,35,69,19)(8,71,76,33,77,28)(9,68,64,25,43,62)(11,15)(12,31,17,38,63,47)(16,41,80,21,24,46)(20,74)(22,67,27)(26,73,37,50,81,57)(29,36,42,54,79,56)(53,65)(58,59,75)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 6D | $6$ | $8640$ | $C_6\times S_3$ | 3A | 2C | 6D | $(1,32,52,23,78,59)(2,42,14,62,67,4)(3,71,75,28,10,33)(5,74,80,15,37,51)(6,56,77,36,17,54)(7,34,22,79,55,68)(8,39,63,60,45,30)(9,18,64,76,43,12)(11,81,65,49,72,24)(13,66,61,29,27,25)(16,48,26,53,69,20)(19,50,46)(21,35,73)(31,70,47,40,38,58)(41,44,57)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 6E | $6$ | $17280$ | $C_3\times C_6$ | 3C | 2B | 6E | $(1,31,26)(2,52,50,8,71,72)(3,64,61,39,23,45)(4,5,24)(6,18,37,27,13,81)(7,77,20,12,14,57)(9,60,78,58,70,47)(10,69,41,43,49,51)(11,80,30,44,16,59)(15,21,40,19,65,54)(17,34,75,55,42,36)(22,74,33,63,73,38)(25,79,28)(29,48,53,68,35,46)(32,66,76,56,62,67)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8A1 | $8$ | $1620$ | $\GL(2,3):C_4$ | 4B | 8A1 | 8A-1 | $(1,18,75,55,80,15,39,50)(2,52,23,45,41,5,56,72)(3,57,6,31,60,67,53,69)(4,43,59,10,68,40,54,30)(7,77,36,28,46,48,32,81)(8,22,70,47,65,19,9,26)(11,42,20,12,63,79,17,51)(13,66,61,21,35,25,73,27)(14,64,76,24,44,58,74,33)(16,49,34,37,38,71,62,78)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8A-1 | $8$ | $1620$ | $\GL(2,3):C_4$ | 4B | 8A-1 | 8A1 | $(1,50,39,15,80,55,75,18)(2,72,56,5,41,45,23,52)(3,69,53,67,60,31,6,57)(4,30,54,40,68,10,59,43)(7,81,32,48,46,28,36,77)(8,26,9,19,65,47,70,22)(11,51,17,79,63,12,20,42)(13,27,73,25,35,21,61,66)(14,33,74,58,44,24,76,64)(16,78,62,71,38,37,34,49)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8B1 | $8$ | $6480$ | $S_3\times C_8$ | 4A | 8B1 | 8B-1 | $(1,55)(2,49,57,66,28,40,9,51)(3,8,36,23,19,31,72,48)(4,12,20,71,38,25,35,43)(5,62,53,73,7,59,47,63)(6,33,46,58,26,24,52,64)(10,65,79,56,78,69,27,77)(11,76,34,14,61,74,54,44)(13,42,68,37,17,21,16,30)(15,80)(22,41,45,67,60,81,32,70)(29,75)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8B-1 | $8$ | $6480$ | $S_3\times C_8$ | 4A | 8B-1 | 8B1 | $(1,55)(2,51,9,40,28,66,57,49)(3,48,72,31,19,23,36,8)(4,43,35,25,38,71,20,12)(5,63,47,59,7,73,53,62)(6,64,52,24,26,58,46,33)(10,77,27,69,78,56,79,65)(11,44,54,74,61,14,34,76)(13,30,16,21,17,37,68,42)(15,80)(22,70,32,81,60,67,45,41)(29,75)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8C | $8$ | $9720$ | $C_4\times C_8$ | 4B | 8C | 8C | $(1,70,68,32,24,56,29,60)(2,67,42,14,46,50,62,19)(3,74,73,39,64,17,55,23)(5,57,59,45,31,61,30,20)(6,41,69,49,51,27,71,52)(7,12,81,47,21,65,78,37)(8,15,66,72,53,77,34,76)(9,58,44,18,75,36,13,11)(10,38,25,33,43,80,79,16)(22,26,63,54,35,28,48,40)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8D | $8$ | $19440$ | $C_2\times C_8$ | 4B | 8D | 8D | $(1,56,6,51,35,42,5,67)(2,31,30,12,15,50,79,49)(3,70,75,10,32,40,59,23)(4,26,7,38,36,63,11,19)(8,74,41,29,69,14,28,64)(9,17,48,46,25,80,27,47)(13,33,54,76,20,44,62,24)(16,61,52,60,45,53,73,68)(18,65,21,66,81,55,78,43)(22,71,39,77,72,57,34,37)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 8E | $8$ | $38880$ | $C_8$ | 4E | 8E | 8E | $(1,45,28,40,33,22,52,46)(2,32,21,13,6,35,59,76)(3,48,7,4,44,39,8,80)(5,53,72,25,42,30,64,69)(9,31,26,71,11,47,66,78)(10,14,61,57,41,17,18,75)(12,20,70,79,27,60,50,81)(15,63,34,23,56,55,49,73)(16,68,74,43,29,24,36,65)(19,62,77,54,58,37,67,51)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 10A | $10$ | $31104$ | $C_{10}$ | 5A | 10A | 2A | $(1,5,16,28,27,77,64,56,45,13)(2,58,8,6,40,22,53,71,52,20)(3,24,60,74,46,65,39,49,59,34)(4,55,35,32,10,57,67,66,51,72)(7,37,50,19,26,14,43,68,79,54)(9,75,15,69,12,80,11,23,36,31)(17,25,81,42,63,78,21,30,41,33)(18,48,76,73,62,38,70,47,29,44)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 12A | $12$ | $4320$ | $C_3:C_{24}$ | 6A | 4A | 12A | $(1,80,29)(2,77,62,57,65,73,28,56,59,9,69,63)(3,32,76,36,22,14,19,45,74,72,60,44)(4,64,68,20,33,17,38,58,16,35,24,13)(5,49,10,53,66,79,7,40,78,47,51,27)(6,37,71,46,21,25,26,30,43,52,42,12)(8,70,34,23,41,61,31,67,54,48,81,11)(15,75,55)(18,50,39)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 12B | $12$ | $12960$ | $C_{24}$ | 6B | 4B | 12B | $(1,78,79,75,49,51,80,37,42,39,71,12)(2,53,77,23,3,28,41,6,48,56,60,81)(4,73,14,59,13,76,68,61,44,54,35,74)(5,31,32,72,67,7,52,69,36,45,57,46)(8,9,65,70)(10,66,24,40,21,58,30,25,33,43,27,64)(11,15,38,20,50,62,63,18,16,17,55,34)(19,47,22,26)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 12C | $12$ | $25920$ | $C_{12}$ | 6B | 4C | 12C | $(1,15,27,4,38,72,2,34,33,53,7,66)(3,73,24,56,75,46,49,60,10,44,81,43)(5,54,59,50,37,39,32,41,80,64,23,35)(6,77,12,76)(9,40,21,26,36,58,19,16,30,70,57,69)(11,55,68,52,20,61,25,31,51,67,62,71)(13,79,47,48,14,29,28,74,22,42,78,65)(17,45,18,63)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 24A1 | $24$ | $12960$ | $C_{24}$ | 12B | 8A1 | 24A-1 | $(1,63,78,18,79,16,75,17,49,55,51,34,80,11,37,15,42,38,39,20,71,50,12,62)(2,7,53,52,77,69,23,36,3,45,28,57,41,46,6,5,48,31,56,32,60,72,81,67)(4,33,73,43,14,27,59,64,13,10,76,66,68,24,61,40,44,21,54,58,35,30,74,25)(8,47,9,22,65,26,70,19)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 24A-1 | $24$ | $12960$ | $C_{24}$ | 12B | 8A-1 | 24A1 | $(1,62,12,50,71,20,39,38,42,15,37,11,80,34,51,55,49,17,75,16,79,18,78,63)(2,67,81,72,60,32,56,31,48,5,6,46,41,57,28,45,3,36,23,69,77,52,53,7)(4,25,74,30,35,58,54,21,44,40,61,24,68,66,76,10,13,64,59,27,14,43,73,33)(8,19,70,26,65,22,9,47)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 24B1 | $24$ | $12960$ | $C_{24}$ | 12A | 8B1 | 24B-1 | $(1,75,80,55,29,15)(2,5,77,49,62,10,57,53,65,66,73,79,28,7,56,40,59,78,9,47,69,51,63,27)(3,11,32,8,76,70,36,34,22,23,14,41,19,61,45,31,74,67,72,54,60,48,44,81)(4,42,64,12,68,6,20,37,33,71,17,46,38,21,58,25,16,26,35,30,24,43,13,52)(18,39,50)$ |
| $C_3^3:S_3.C_2^4:S_5$ | 24B-1 | $24$ | $12960$ | $C_{24}$ | 12A | 8B-1 | 24B1 | $(1,15,29,55,80,75)(2,27,63,51,69,47,9,78,59,40,56,7,28,79,73,66,65,53,57,10,62,49,77,5)(3,81,44,48,60,54,72,67,74,31,45,61,19,41,14,23,22,34,36,70,76,8,32,11)(4,52,13,43,24,30,35,26,16,25,58,21,38,46,17,71,33,37,20,6,68,12,64,42)(18,50,39)$ |