Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C29 |
| direct product | C19×#34312 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#548 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2960 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)(20,21,23,22)(25,27)(28,29,34,32)(30,37,31,35)(33,40,41,36)(38,42,39,43);(28,30,34,31)(29,35,32,37)(33,38,41,39)(36,42,40,43);(24,25,26,27)(28,31,34,30)(29,35,32,37)(33,39,41,38)(36,42,40,43);(28,32,34,29)(30,35,31,37)(33,40,41,36)(38,42,39,43);(20,22,23,21)(28,33,34,41)(29,36,32,40)(30,38,31,39)(35,42,37,43)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27300);