Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#24854 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
788 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,28,31)(26,30,27,29)(32,33,38,46,37,42,36,41)(34,39,43,47,35,45,44,40);(20,21)(22,23)(24,26,28,27)(25,29,31,30)(32,34)(33,39)(35,37)(36,44)(38,43)(40,41)(42,45)(46,47);(21,23)(32,35,37,34)(33,40,42,47)(36,44,38,43)(39,46,45,41);(24,27,28,26)(25,30,31,29)(32,36,37,38)(33,41,42,46)(34,43,35,44)(39,47,45,40)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17842);