Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
470 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)(28,29,33,37,34,38,32,48)(30,39,43,50,42,54,41,35)(31,44,46,52,47,36,45,51)(40,53,57,49,56,59,55,58);(21,25)(22,23)(26,27)(28,30)(29,35,38,50)(31,40)(32,41)(33,43)(34,42)(36,49,44,58)(37,39,48,54)(45,55)(46,57)(47,56)(51,59,52,53);(21,25)(22,23)(26,27)(28,31,34,47)(29,36,38,44)(30,40,42,56)(32,46,33,45)(35,49,50,58)(37,52,48,51)(39,53,54,59)(41,57,43,55)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2284);