Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8413 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#3518 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(21,24,25,26)(28,29)(30,38,41,34)(31,42,44,51)(32,37)(33,36)(35,43,49,45)(39,54)(40,53,58,48)(46,50)(47,55)(52,57)(56,59);(20,21)(22,26)(23,25)(24,27)(28,30)(29,34)(31,39)(32,40)(33,41)(35,47)(36,38)(37,48)(42,59)(43,55)(44,56)(45,57)(46,58)(49,52)(50,53)(51,54);(28,31,33,44)(29,35,36,49)(30,39,41,56)(32,45,46,43)(34,47,38,52)(37,51,50,42)(40,57,58,55)(48,54,53,59)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1401);