Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C8 |
| direct product | C19×#8793 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #382 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #124 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
294 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)(21,22)(23,24)(26,27)(28,29)(30,38,42,34)(31,43,45,58)(32,37)(33,36)(35,44,49,53)(39,46)(40,54)(41,51,52,48)(47,55)(50,59)(56,57);(20,21,23,22,25,27,24,26)(28,30,39,52,33,42,32,41)(29,34,46,51,36,38,37,48)(31,40,53,59,45,56,44,55)(35,47,58,54,49,50,43,57);(20,22,24,21,25,26,23,27)(28,31,33,45)(29,35)(30,40,42,56)(32,44,39,53)(34,47)(36,49)(37,43)(38,50)(41,55,52,59)(46,58)(48,57)(51,54)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1781);