Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18928 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3506 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
966 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,23)(26,27)(28,29,33,37)(30,38,39,42)(31,36,32,35)(34,41,43,40);(20,21,24,27)(22,25,23,26)(28,30,33,39)(29,34,37,43)(31,41,32,40)(35,42,36,38);(20,22,24,23)(21,25,27,26)(29,35)(31,32)(34,42)(36,37)(38,43)(40,41);(20,22,24,23)(21,26,27,25)(30,39)(34,43)(38,42)(40,41)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11916);