Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10169 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×C19×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
556 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
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)(20,21)(22,25)(23,27)(24,26)(28,29,33,37)(30,38,41,42)(31,34,32,36)(35,39,43,40);(21,25)(22,24)(26,27)(29,34)(30,39)(31,32)(36,37)(38,42)(40,41);(20,21,23,27)(22,25,24,26)(28,30,33,41)(29,35,37,43)(31,39,32,40)(34,38,36,42)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3157);