Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
318 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)(20,21,24,26)(22,27,23,25)(28,29)(30,34)(31,35)(32,37)(33,39)(36,44)(38,45)(40,53)(41,50)(42,48)(43,49)(46,52)(47,54)(51,57)(55,59)(56,58);(20,22,24,23)(21,25,26,27)(28,30)(29,34)(31,41)(32,40)(33,43)(35,50)(36,47)(37,53)(38,48)(39,49)(42,45)(44,54)(46,55)(51,58)(52,59)(56,57);(20,23,24,22)(21,25,26,27)(29,35)(30,40)(31,44)(32,45)(34,47)(36,38)(37,51)(39,52)(41,55)(42,43)(46,57)(48,59)(49,58)(50,53)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6443);