Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C29 |
| direct product | C19×#34182 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2858 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)(24,25,26,27)(29,30)(32,40)(34,36)(38,43);(28,29,33,30)(31,36,39,34)(32,35,40,37)(38,42,43,41);(20,21,22,23)(28,30,33,29)(31,36,39,34)(32,37,40,35)(38,42,43,41);(28,31,33,39)(29,34,30,36)(32,38,40,43)(35,41,37,42);(28,32)(29,35)(30,37)(31,38)(33,40)(34,41)(36,42)(39,43)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27170);