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×#33676 |
| 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 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
548 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)(28,29,34,39)(30,35,43,51)(31,37,33,47)(32,36,46,53)(38,44,52,45)(40,49,42,57)(41,48,56,59)(50,54,58,55);(21,24)(25,27)(28,30,34,43)(29,35,39,51)(31,40,33,42)(32,41,46,56)(36,48,53,59)(37,49,47,57)(38,50,52,58)(44,54,45,55);(29,36)(31,33)(32,45)(35,48)(37,38)(39,53)(40,42)(41,55)(44,46)(47,52)(49,50)(51,59)(54,56)(57,58);(20,22,23,26)(21,25,24,27)(28,31,34,33)(29,37,39,47)(30,40,43,42)(32,44,46,45)(35,49,51,57)(36,52,53,38)(41,54,56,55)(48,58,59,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26664);