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×#33649 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C24×C19 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
580 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)(28,29,34,39)(30,40,43,57)(31,38,33,36)(32,45,48,53)(35,50,52,42)(37,44,55,47)(41,58,49,54)(46,56,59,51);(21,24)(25,27);(20,22,23,26)(21,25,24,27)(28,30)(29,35)(31,41)(32,46)(33,49)(34,43)(36,51)(37,54)(38,56)(39,52)(40,45)(42,47)(44,50)(48,59)(53,57)(55,58);(28,31,34,33)(29,36,39,38)(30,41,43,49)(32,44,48,47)(35,51,52,56)(37,53,55,45)(40,54,57,58)(42,46,50,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26637);