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×#33680 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
534 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)(28,29,33,38)(30,34,39,47)(31,35,44,51)(32,45,43,37)(36,52,50,42)(40,46,53,57)(41,56,54,49)(48,59,58,55);(21,24)(25,27)(28,30,33,39)(29,34,38,47)(31,40,44,53)(32,41,43,54)(35,46,51,57)(36,48,50,58)(37,49,45,56)(42,55,52,59);(29,35)(31,42)(32,43)(34,46)(36,37)(38,51)(40,55)(41,54)(44,52)(45,50)(47,57)(48,49)(53,59)(56,58);(20,22,23,26)(21,25,24,27)(30,39)(34,47)(40,53)(41,54)(46,57)(48,58)(49,56)(55,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26668);