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×#35030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C19×#2416 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1964 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)(28,29,32,30)(31,34,35,33)(36,37,41,43)(38,40,42,39);(21,24)(25,27)(29,30)(33,34)(36,38,41,42)(37,39,43,40);(20,21)(22,25)(23,24)(26,27)(28,29,32,30)(31,33,35,34)(36,37)(38,39)(40,42)(41,43);(20,21)(22,25)(23,24)(26,27)(28,30,32,29)(31,34,35,33)(36,39,41,40)(37,38,43,42);(20,22)(21,25)(23,26)(24,27)(28,31,32,35)(29,33,30,34)(36,40,41,39)(37,42,43,38)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 28018);