Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#23668 |
| 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 | |
874 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)(26,31)(27,29)(28,30)(32,33,37,39,36,41,35,40)(34,38,44,45,42,46,43,47);(20,21)(22,23)(24,26,28,27)(25,29,30,31)(32,34)(33,38)(35,43)(36,42)(37,44)(39,45)(40,47)(41,46);(21,23)(24,27,28,26)(25,29,30,31)(33,39)(35,37)(38,45)(40,41)(43,44)(46,47);(34,42)(38,46)(43,44)(45,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16656);