Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10013 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #392 |
| prime radical | C19×#3100 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
598 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)(21,24)(22,26)(25,27)(28,29)(30,36)(31,39)(32,35)(33,37)(34,41)(38,43)(40,42);(20,21,23,25)(22,27,26,24)(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36);(20,21)(22,27)(23,25)(24,26)(33,42)(36,43)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3001);