Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11932 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 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)(30,39)(31,36)(32,45)(33,49)(34,38)(35,41)(37,47)(40,53)(42,59)(43,56)(44,54)(46,52)(48,55)(50,57)(51,58);(21,24)(22,26)(28,30,34,43)(29,35,38,51)(31,42,33,40)(32,46,48,57)(36,52,49,50)(37,53,54,59)(39,55,56,45)(41,44,58,47);(28,31,34,33)(29,36,38,49)(30,40,43,42)(32,44,48,47)(35,50,51,52)(37,45,54,55)(39,53,56,59)(41,57,58,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4920);