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) = C25 |
| direct product | C19×#8429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#3497 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
936 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)(20,21,23,25,24,27,22,26)(28,29,33,39,34,37,32,38)(30,40,42,53,43,35,48,50)(31,44,46,36,47,52,45,51)(41,55,56,49,57,59,58,54);(21,25)(22,23)(26,27)(28,30)(29,35)(31,41)(32,42)(33,48)(34,43)(36,49)(37,40)(38,50)(39,53)(44,59)(45,56)(46,58)(47,57)(51,54)(52,55);(28,31,34,47)(29,36,37,51)(30,41,43,57)(32,46,33,45)(35,49,40,54)(38,52,39,44)(42,58,48,56)(50,55,53,59)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1417);