Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C28×C4 |
| direct product | C19×#34641 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
3694 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)(21,23)(25,27)(28,29)(30,33)(31,35)(32,34)(36,39)(37,40)(38,41)(42,43);(20,21,22,23)(28,30)(29,33)(31,37)(32,36)(34,39)(35,40)(38,42)(41,43);(24,25,26,27)(30,36)(33,39)(37,42)(40,43);(29,34)(33,39)(35,41)(40,43);(28,31,32,38)(29,35,34,41)(30,37,36,42)(33,40,39,43)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27629);