Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| isoclinism | isoclinic class of #72209600 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #585 ⋊ A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #11757162 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | #585 | A5 |
| socle | C2 | #14515300 |
| LCS | G | |
| UCS | C1 ◁ C4 | |
246 conjugacy classes of subgroups; only the 5 normal subgroups are shown.
This group has 246 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)(8,29)(9,31)(10,21)(11,22)(12,17)(13,23)(14,24)(16,44)(18,25)(19,26)(20,27)(30,57)(32,53)(34,50)(35,52)(36,47)(37,43)(38,48)(39,56)(40,45)(41,46)(42,51)(54,55)(58,64)(59,62)(61,63);(2,8,9)(3,15,16)(4,21,5)(10,37,17)(11,40,34)(12,30,44)(13,25,35)(14,18,36)(19,33,42)(20,49,48)(22,53,39)(23,50,26)(24,56,27)(29,57,46)(31,58,59)(32,52,38)(41,63,54)(43,62,61)(45,47,51)(55,60,64);(1,2)(3,10)(4,22)(5,12)(6,13)(7,14)(8,9)(11,41)(15,47)(16,50)(17,51)(18,36)(19,34)(20,39)(21,48)(23,37)(24,43)(25,35)(26,45)(27,32)(28,46)(29,57)(30,49)(31,33)(38,62)(40,58)(42,63)(44,53)(52,60)(54,59)(55,61)(56,64);(1,3)(2,10)(4,17)(5,25)(6,19)(7,20)(8,27)(9,32)(11,38)(12,35)(13,34)(14,39)(15,48)(16,33)(18,54)(21,47)(22,51)(23,40)(24,53)(26,29)(28,55)(30,56)(31,50)(36,59)(37,58)(41,62)(42,60)(43,44)(45,57)(46,61)(49,64)(52,63);(1,4)(2,11)(3,17)(5,21)(6,23)(7,24)(8,30)(9,33)(10,38)(12,42)(13,43)(14,37)(15,36)(16,32)(18,52)(19,40)(20,53)(22,46)(25,47)(26,50)(27,56)(28,41)(29,31)(34,44)(35,60)(39,58)(45,64)(48,59)(49,57)(51,61)(54,63)(55,62);(1,5)(2,12)(3,18)(4,21)(6,26)(7,27)(8,19)(9,34)(10,36)(11,42)(13,45)(14,32)(15,38)(16,37)(17,52)(20,29)(22,48)(23,50)(24,56)(25,55)(28,54)(30,40)(31,53)(33,44)(35,61)(39,57)(41,63)(43,64)(46,59)(47,62)(49,58)(51,60);(1,6,28,7)(2,13,46,14)(3,19,55,20)(4,23,41,24)(5,26,54,27)(8,25,29,18)(9,35,57,36)(10,34,61,39)(11,43,22,37)(12,45,59,32)(15,33,60,49)(16,42,64,48)(17,40,62,53)(21,50,63,56)(30,47,31,52)(38,44,51,58)24 conjugacy classes — view the full character table.
| maximal subgroup of | #72209929, #72265798, #72266252, … |
| maximal quotient of | #72209624, #72209626, #72209630, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,4)(3,5)(8,29)(9,31)(10,21)(11,22)(12,17)(13,23)(14,24)(16,44)(18,25)(19,26)(20,27)(30,57)(32,53)(34,50)(35,52)(36,47)(37,43)(38,48)(39,56)(40,45)(41,46)(42,51)(54,55)(58,64)(59,62)(61,63), (2,8,9)(3,15,16)(4,21,5)(10,37,17)(11,40,34)(12,30,44)(13,25,35)(14,18,36)(19,33,42)(20,49,48)(22,53,39)(23,50,26)(24,56,27)(29,57,46)(31,58,59)(32,52,38)(41,63,54)(43,62,61)(45,47,51)(55,60,64), (1,2)(3,10)(4,22)(5,12)(6,13)(7,14)(8,9)(11,41)(15,47)(16,50)(17,51)(18,36)(19,34)(20,39)(21,48)(23,37)(24,43)(25,35)(26,45)(27,32)(28,46)(29,57)(30,49)(31,33)(38,62)(40,58)(42,63)(44,53)(52,60)(54,59)(55,61)(56,64), (1,3)(2,10)(4,17)(5,25)(6,19)(7,20)(8,27)(9,32)(11,38)(12,35)(13,34)(14,39)(15,48)(16,33)(18,54)(21,47)(22,51)(23,40)(24,53)(26,29)(28,55)(30,56)(31,50)(36,59)(37,58)(41,62)(42,60)(43,44)(45,57)(46,61)(49,64)(52,63), (1,4)(2,11)(3,17)(5,21)(6,23)(7,24)(8,30)(9,33)(10,38)(12,42)(13,43)(14,37)(15,36)(16,32)(18,52)(19,40)(20,53)(22,46)(25,47)(26,50)(27,56)(28,41)(29,31)(34,44)(35,60)(39,58)(45,64)(48,59)(49,57)(51,61)(54,63)(55,62), (1,5)(2,12)(3,18)(4,21)(6,26)(7,27)(8,19)(9,34)(10,36)(11,42)(13,45)(14,32)(15,38)(16,37)(17,52)(20,29)(22,48)(23,50)(24,56)(25,55)(28,54)(30,40)(31,53)(33,44)(35,61)(39,57)(41,63)(43,64)(46,59)(47,62)(49,58)(51,60), (1,6,28,7)(2,13,46,14)(3,19,55,20)(4,23,41,24)(5,26,54,27)(8,25,29,18)(9,35,57,36)(10,34,61,39)(11,43,22,37)(12,45,59,32)(15,33,60,49)(16,42,64,48)(17,40,62,53)(21,50,63,56)(30,47,31,52)(38,44,51,58));