Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33632 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(30,38)(31,41)(32,43)(34,46)(36,51)(37,50)(39,56)(40,55)(42,45)(44,54)(47,58)(48,59)(49,57)(52,53);(20,22,23,27)(21,24,25,26)(28,29)(30,34)(31,36)(32,37)(33,35)(38,46)(39,48)(40,47)(41,51)(42,52)(43,50)(44,49)(45,53)(54,57)(55,58)(56,59);(28,30,33,40)(29,34,35,47)(31,42,44,56)(32,45,43,39)(36,52,49,59)(37,53,50,48)(38,54,55,41)(46,57,58,51);(29,35)(34,47)(36,49)(37,50)(46,58)(48,53)(51,57)(52,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26620);