Finite Group DatabasebetaFinite Group Databasebeta| order | 60480 |
| isoclinism | isoclinic class of SL(3,𝔽4) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C42 |
| special linear | SL(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, cosocle, hypercenter | C3 | PSL(3,𝔽4) |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 ◁ C3 | |
200 conjugacy classes of subgroups.
Permutation generators:
(1,5)(2,10)(3,15)(6,14)(7,11)(9,13)(17,21)(18,26)(19,31)(22,30)(23,27)(25,29)(33,37)(34,42)(35,47)(38,46)(39,43)(41,45)(49,53)(50,58)(51,63)(54,62)(55,59)(57,61);(4,5)(6,7)(8,10)(9,11)(12,15)(13,14)(20,21)(22,23)(24,26)(25,27)(28,31)(29,30)(36,37)(38,39)(40,42)(41,43)(44,47)(45,46)(52,53)(54,55)(56,58)(57,59)(60,63)(61,62);(1,9)(2,14)(3,7)(5,13)(6,10)(11,15)(17,25)(18,30)(19,23)(21,29)(22,26)(27,31)(33,41)(34,46)(35,39)(37,45)(38,42)(43,47)(49,57)(50,62)(51,55)(53,61)(54,58)(59,63);(4,6)(5,7)(8,11)(9,10)(12,13)(14,15)(20,22)(21,23)(24,27)(25,26)(28,29)(30,31)(36,38)(37,39)(40,43)(41,42)(44,45)(46,47)(52,54)(53,55)(56,59)(57,58)(60,61)(62,63);(4,20)(5,21)(6,22)(7,23)(8,40)(9,41)(10,42)(11,43)(12,60)(13,61)(14,62)(15,63)(24,56)(25,57)(26,58)(27,59)(28,44)(29,45)(30,46)(31,47)(36,52)(37,53)(38,54)(39,55);(16,20)(17,21)(18,22)(19,23)(24,28)(25,29)(26,30)(27,31)(32,40)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(48,60)(49,61)(50,62)(51,63)(52,56)(53,57)(54,58)(55,59);(4,36)(5,37)(6,38)(7,39)(8,56)(9,57)(10,58)(11,59)(12,28)(13,29)(14,30)(15,31)(20,52)(21,53)(22,54)(23,55)(24,40)(25,41)(26,42)(27,43)(44,60)(45,61)(46,62)(47,63);(16,24)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(32,44)(33,45)(34,46)(35,47)(36,40)(37,41)(38,42)(39,43)(48,52)(49,53)(50,54)(51,55)(56,60)(57,61)(58,62)(59,63)28 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,5)(2,10)(3,15)(6,14)(7,11)(9,13)(17,21)(18,26)(19,31)(22,30)(23,27)(25,29)(33,37)(34,42)(35,47)(38,46)(39,43)(41,45)(49,53)(50,58)(51,63)(54,62)(55,59)(57,61), (4,5)(6,7)(8,10)(9,11)(12,15)(13,14)(20,21)(22,23)(24,26)(25,27)(28,31)(29,30)(36,37)(38,39)(40,42)(41,43)(44,47)(45,46)(52,53)(54,55)(56,58)(57,59)(60,63)(61,62), (1,9)(2,14)(3,7)(5,13)(6,10)(11,15)(17,25)(18,30)(19,23)(21,29)(22,26)(27,31)(33,41)(34,46)(35,39)(37,45)(38,42)(43,47)(49,57)(50,62)(51,55)(53,61)(54,58)(59,63), (4,6)(5,7)(8,11)(9,10)(12,13)(14,15)(20,22)(21,23)(24,27)(25,26)(28,29)(30,31)(36,38)(37,39)(40,43)(41,42)(44,45)(46,47)(52,54)(53,55)(56,59)(57,58)(60,61)(62,63), (4,20)(5,21)(6,22)(7,23)(8,40)(9,41)(10,42)(11,43)(12,60)(13,61)(14,62)(15,63)(24,56)(25,57)(26,58)(27,59)(28,44)(29,45)(30,46)(31,47)(36,52)(37,53)(38,54)(39,55), (16,20)(17,21)(18,22)(19,23)(24,28)(25,29)(26,30)(27,31)(32,40)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(48,60)(49,61)(50,62)(51,63)(52,56)(53,57)(54,58)(55,59), (4,36)(5,37)(6,38)(7,39)(8,56)(9,57)(10,58)(11,59)(12,28)(13,29)(14,30)(15,31)(20,52)(21,53)(22,54)(23,55)(24,40)(25,41)(26,42)(27,43)(44,60)(45,61)(46,62)(47,63), (16,24)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(32,44)(33,45)(34,46)(35,47)(36,40)(37,41)(38,42)(39,43)(48,52)(49,53)(50,54)(51,55)(56,60)(57,61)(58,62)(59,63));