Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10631 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#10633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #397 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #124 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(28,29,32,34,33,37,31,36)(30,38,40,43,39,42,41,35);(20,21,23,26)(22,24,27,25)(29,34)(30,39)(31,32)(35,42)(36,37)(38,43);(21,24)(22,27)(25,26)(28,30,31,40,33,39,32,41)(29,35,36,38,37,43,34,42)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3621);