Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C8 |
| direct product | C19×#19721 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
798 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(20,21,26,22)(23,24,27,25)(28,29,34,38)(30,39,42,43)(31,36,35,41)(32,37,33,40);(20,22,24,27,26,21,25,23)(28,30,33,36,34,42,32,41)(29,35,37,39,38,31,40,43);(20,23,25,21,26,27,24,22)(28,31)(29,36)(30,40)(32,39)(33,43)(34,35)(37,42)(38,41);(20,24,26,25)(21,27,22,23)(28,32,34,33)(29,37,38,40)(30,41,42,36)(31,43,35,39)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12709);