Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#35026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(22,26)(25,27)(28,29,33,32)(30,35,31,34)(36,37,39,41)(38,40,42,43);(21,24)(25,27)(28,30,33,31)(29,34,32,35)(36,37)(38,40)(39,41)(42,43);(20,21)(22,25)(23,24)(26,27)(28,31,33,30)(29,35,32,34);(20,21)(22,25)(23,24)(26,27);(20,22)(21,25)(23,26)(24,27)(28,32,33,29)(30,35,31,34)(36,38,39,42)(37,40,41,43)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 28014);