Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22×C8 |
| direct product | C19×#12515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C19 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C82×C19 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,25)(26,27)(29,33)(30,34)(31,37)(35,43)(36,41)(38,42)(39,40);(28,29,34,40,31,35,38,41,32,36,42,43,37,39,30,33);(20,21,25,27,23,26,22,24)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5503);