Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #585 ⋊ A5 |
| derived | 2−1+4⋊A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11757163 |
| commutator, hypocenter | 2−1+4⋊A5 | C2 |
| Frattini, socle | C2 | C2×#11757163 |
| Fitting | #585 | A5 |
| cosocle | 2−1+4 | C2×A5 |
| LCS | G ▷ 2−1+4⋊A5 | |
| UCS | C1 ◁ C4 | |
275 conjugacy classes of subgroups; only the 7 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 7 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(2,22,40,58,28)(3,4,8,63,11)(5,17,18,14,12)(9,61,57,47,33)(10,34,50,64,23)(13,44,42,15,55)(16,56,24,43,52)(19,38,45,21,26)(20,25,29,39,41)(27,60,62,59,51)(30,36,48,49,37)(31,54,53,35,46);(3,8,51)(5,57,33)(9,62,12)(10,34,64)(11,27,18)(14,59,63)(17,60,61)(19,30,21)(20,29,31)(22,58,28)(35,37,38)(36,53,45)(39,49,46)(41,54,48)(42,55,44)(43,52,56);(1,32)(2,50)(3,57)(4,47)(5,51)(6,7)(8,33)(9,63)(10,58)(11,61)(12,59)(13,24)(14,62)(15,16)(17,27)(18,60)(19,29)(20,21)(22,64)(23,40)(25,26)(28,34)(30,31)(35,49)(36,54)(37,46)(38,39)(41,45)(42,52)(43,44)(48,53)(55,56);(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);(1,20,32,21)(2,37,50,46)(3,6,57,7)(4,43,47,44)(5,33,51,8)(9,14,63,62)(10,25,58,26)(11,24,61,13)(12,15,59,16)(17,18,27,60)(19,31,29,30)(22,28,64,34)(23,41,40,45)(35,38,49,39)(36,48,54,53)(42,56,52,55);(1,25,32,26)(2,23,50,40)(3,43,57,44)(4,6,47,7)(5,55,51,56)(8,52,33,42)(9,27,63,17)(10,20,58,21)(11,59,61,12)(13,15,24,16)(14,60,62,18)(19,34,29,28)(22,30,64,31)(35,48,49,53)(36,38,54,39)(37,41,46,45);(1,30,32,31)(2,49,50,35)(3,8,57,33)(4,55,47,56)(5,6,51,7)(9,59,63,12)(10,34,58,28)(11,27,61,17)(13,60,24,18)(14,15,62,16)(19,20,29,21)(22,25,64,26)(23,53,40,48)(36,41,54,45)(37,38,46,39)(42,43,52,44);(1,3,35,63,32,57,49,9)(2,47,31,18,50,4,30,60)(5,48,16,25,51,53,15,26)(6,20,14,39,7,21,62,38)(8,58,12,54,33,10,59,36)(11,40,52,22,61,23,42,64)(13,28,55,45,24,34,56,41)(17,19,43,46,27,29,44,37)32 conjugacy classes — view the full character table.
| maximal subgroup of | #72209929, #72268585, #72288038 |
| maximal quotient of | #72227889 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,22,40,58,28)(3,4,8,63,11)(5,17,18,14,12)(9,61,57,47,33)(10,34,50,64,23)(13,44,42,15,55)(16,56,24,43,52)(19,38,45,21,26)(20,25,29,39,41)(27,60,62,59,51)(30,36,48,49,37)(31,54,53,35,46), (3,8,51)(5,57,33)(9,62,12)(10,34,64)(11,27,18)(14,59,63)(17,60,61)(19,30,21)(20,29,31)(22,58,28)(35,37,38)(36,53,45)(39,49,46)(41,54,48)(42,55,44)(43,52,56), (1,32)(2,50)(3,57)(4,47)(5,51)(6,7)(8,33)(9,63)(10,58)(11,61)(12,59)(13,24)(14,62)(15,16)(17,27)(18,60)(19,29)(20,21)(22,64)(23,40)(25,26)(28,34)(30,31)(35,49)(36,54)(37,46)(38,39)(41,45)(42,52)(43,44)(48,53)(55,56), (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), (1,20,32,21)(2,37,50,46)(3,6,57,7)(4,43,47,44)(5,33,51,8)(9,14,63,62)(10,25,58,26)(11,24,61,13)(12,15,59,16)(17,18,27,60)(19,31,29,30)(22,28,64,34)(23,41,40,45)(35,38,49,39)(36,48,54,53)(42,56,52,55), (1,25,32,26)(2,23,50,40)(3,43,57,44)(4,6,47,7)(5,55,51,56)(8,52,33,42)(9,27,63,17)(10,20,58,21)(11,59,61,12)(13,15,24,16)(14,60,62,18)(19,34,29,28)(22,30,64,31)(35,48,49,53)(36,38,54,39)(37,41,46,45), (1,30,32,31)(2,49,50,35)(3,8,57,33)(4,55,47,56)(5,6,51,7)(9,59,63,12)(10,34,58,28)(11,27,61,17)(13,60,24,18)(14,15,62,16)(19,20,29,21)(22,25,64,26)(23,53,40,48)(36,41,54,45)(37,38,46,39)(42,43,52,44), (1,3,35,63,32,57,49,9)(2,47,31,18,50,4,30,60)(5,48,16,25,51,53,15,26)(6,20,14,39,7,21,62,38)(8,58,12,54,33,10,59,36)(11,40,52,22,61,23,42,64)(13,28,55,45,24,34,56,41)(17,19,43,46,27,29,44,37));