Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23427 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×C19×#135 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1986 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)(22,23)(28,29)(30,37)(31,39)(32,35)(33,42)(34,36)(38,41)(40,43);(21,23)(24,25)(26,27)(28,30,34,40)(29,31,36,41)(32,39,33,38)(35,43,42,37);(25,27)(28,31)(29,30)(32,37)(33,43)(34,41)(35,38)(36,40)(39,42);(28,32,34,33)(29,35,36,42)(30,38,40,39)(31,37,41,43)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16415);