Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| isoclinism | isoclinic class of #72209929 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | #585 ⋊ A6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #72209614 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | #585 | A6 |
| socle | C2 | #72209666 |
| LCS | G | |
| UCS | C1 ◁ C4 | |
468 conjugacy classes of subgroups; only the 5 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 5 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(2,4)(3,5)(8,33)(9,28)(10,14)(11,18)(12,22)(13,24)(15,25)(16,26)(19,29)(20,30)(21,31)(23,40)(34,63)(35,44)(37,55)(38,42)(39,52)(41,48)(43,49)(45,53)(46,56)(47,50)(51,57)(58,62)(59,64)(60,61);(2,8,9)(3,17,18)(4,22,5)(10,12,40)(11,14,34)(13,43,37)(15,29,38)(16,19,39)(20,36,48)(21,54,53)(23,58,59)(24,44,46)(25,55,30)(26,56,31)(27,60,57)(28,61,62)(33,63,50)(35,42,45)(41,49,52)(47,64,51);(2,10,11)(4,23,12)(5,27,28)(8,18,22)(13,46,26)(15,43,41)(16,44,45)(17,34,51)(19,53,56)(24,37,25)(29,48,55)(30,54,42)(31,36,52)(33,60,64)(40,59,47)(50,58,61);(1,2)(3,12)(4,24)(5,14)(6,15)(7,16)(8,9)(10,41)(11,44)(13,47)(17,52)(18,55)(19,39)(20,37)(21,46)(22,53)(23,26)(25,40)(27,42)(28,36)(29,38)(30,49)(31,35)(32,50)(33,63)(34,54)(43,61)(45,58)(48,64)(51,62)(56,60)(57,59);(1,3)(2,12)(4,10)(5,29)(6,20)(7,21)(8,31)(9,35)(11,23)(13,45)(14,38)(15,37)(16,46)(17,53)(18,36)(19,51)(22,52)(24,41)(25,43)(26,44)(27,48)(28,55)(30,33)(32,57)(34,56)(39,62)(40,61)(42,64)(47,58)(49,63)(50,59)(54,60);(1,4)(2,13)(3,10)(5,22)(6,25)(7,26)(8,34)(9,36)(11,37)(12,45)(14,48)(15,23)(16,40)(17,39)(18,35)(19,42)(20,43)(21,44)(24,50)(27,38)(28,33)(29,52)(30,55)(31,56)(32,47)(41,59)(46,61)(49,60)(51,64)(53,62)(54,63)(57,58);(1,5)(2,14)(3,19)(4,22)(6,30)(7,31)(8,20)(9,37)(10,42)(11,36)(12,39)(13,48)(15,49)(16,35)(17,45)(18,40)(21,33)(23,60)(24,53)(25,55)(26,56)(27,41)(28,44)(29,57)(32,51)(34,43)(38,59)(46,63)(47,64)(50,62)(52,58)(54,61);(1,6,32,7)(2,15,50,16)(3,20,57,21)(4,25,47,26)(5,30,51,31)(8,29,33,19)(9,38,63,39)(10,43,58,44)(11,41,61,45)(12,37,59,46)(13,23,24,40)(14,49,62,35)(17,36,27,54)(18,48,60,53)(22,55,64,56)(28,42,34,52)35 conjugacy classes — view the full character table.
| maximal quotient of | #72227900 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,4)(3,5)(8,33)(9,28)(10,14)(11,18)(12,22)(13,24)(15,25)(16,26)(19,29)(20,30)(21,31)(23,40)(34,63)(35,44)(37,55)(38,42)(39,52)(41,48)(43,49)(45,53)(46,56)(47,50)(51,57)(58,62)(59,64)(60,61), (2,8,9)(3,17,18)(4,22,5)(10,12,40)(11,14,34)(13,43,37)(15,29,38)(16,19,39)(20,36,48)(21,54,53)(23,58,59)(24,44,46)(25,55,30)(26,56,31)(27,60,57)(28,61,62)(33,63,50)(35,42,45)(41,49,52)(47,64,51), (2,10,11)(4,23,12)(5,27,28)(8,18,22)(13,46,26)(15,43,41)(16,44,45)(17,34,51)(19,53,56)(24,37,25)(29,48,55)(30,54,42)(31,36,52)(33,60,64)(40,59,47)(50,58,61), (1,2)(3,12)(4,24)(5,14)(6,15)(7,16)(8,9)(10,41)(11,44)(13,47)(17,52)(18,55)(19,39)(20,37)(21,46)(22,53)(23,26)(25,40)(27,42)(28,36)(29,38)(30,49)(31,35)(32,50)(33,63)(34,54)(43,61)(45,58)(48,64)(51,62)(56,60)(57,59), (1,3)(2,12)(4,10)(5,29)(6,20)(7,21)(8,31)(9,35)(11,23)(13,45)(14,38)(15,37)(16,46)(17,53)(18,36)(19,51)(22,52)(24,41)(25,43)(26,44)(27,48)(28,55)(30,33)(32,57)(34,56)(39,62)(40,61)(42,64)(47,58)(49,63)(50,59)(54,60), (1,4)(2,13)(3,10)(5,22)(6,25)(7,26)(8,34)(9,36)(11,37)(12,45)(14,48)(15,23)(16,40)(17,39)(18,35)(19,42)(20,43)(21,44)(24,50)(27,38)(28,33)(29,52)(30,55)(31,56)(32,47)(41,59)(46,61)(49,60)(51,64)(53,62)(54,63)(57,58), (1,5)(2,14)(3,19)(4,22)(6,30)(7,31)(8,20)(9,37)(10,42)(11,36)(12,39)(13,48)(15,49)(16,35)(17,45)(18,40)(21,33)(23,60)(24,53)(25,55)(26,56)(27,41)(28,44)(29,57)(32,51)(34,43)(38,59)(46,63)(47,64)(50,62)(52,58)(54,61), (1,6,32,7)(2,15,50,16)(3,20,57,21)(4,25,47,26)(5,30,51,31)(8,29,33,19)(9,38,63,39)(10,43,58,44)(11,41,61,45)(12,37,59,46)(13,23,24,40)(14,49,62,35)(17,36,27,54)(18,48,60,53)(22,55,64,56)(28,42,34,52));