Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
516 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)(30,35)(31,41)(32,46)(33,48)(34,38)(36,45)(37,43)(39,53)(40,52)(42,55)(44,56)(47,59)(49,54)(50,57)(51,58);(21,24)(25,27)(28,30,34,33)(29,35,38,48)(31,42,44,39)(32,40,47,43)(36,50,51,49)(37,46,52,59)(41,55,56,53)(45,57,58,54);(28,31,43,57,33,42,47,58,34,44,40,54,30,39,32,45)(29,36,46,53,35,49,52,56,38,51,59,55,48,50,37,41);(20,22,23,26)(21,25,24,27)(31,44)(36,51)(39,42)(41,56)(45,58)(49,50)(53,55)(54,57)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26738);