Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33647 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(30,34)(31,35)(32,45)(33,36)(37,42)(38,43)(39,46)(40,55)(41,47)(44,50)(48,52)(49,53)(51,56)(54,57)(58,59);(21,24)(25,27)(28,30,33,41)(29,34,36,47)(31,39,44,54)(32,40,43,53)(35,46,50,57)(37,48,51,58)(38,49,45,55)(42,52,56,59);(20,22,23,26)(21,25,24,27)(29,35)(31,42)(32,43)(34,46)(36,50)(37,38)(39,52)(40,53)(44,56)(45,51)(47,57)(48,49)(54,59)(55,58);(29,36)(34,47)(35,50)(37,51)(38,45)(46,57)(48,58)(49,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26635);