Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33744 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| 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)(22,25)(23,24)(26,27)(30,38)(31,40)(32,43)(34,45)(36,46)(37,49)(39,50)(41,57)(42,53)(44,56)(47,59)(48,54)(51,52)(55,58);(21,24)(25,27)(28,29)(30,39)(31,36)(32,37)(33,35)(34,42)(38,50)(40,46)(41,55)(43,49)(44,48)(45,53)(47,51)(52,59)(54,56)(57,58);(28,30,40,52,32,41,44,53,33,42,56,57,43,51,31,38)(29,34,46,58,37,47,48,50,35,39,54,59,49,55,36,45);(20,22,23,26)(21,25,24,27)(29,35)(34,39)(36,48)(37,49)(45,50)(46,54)(47,55)(58,59)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26732);