Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24034 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#550 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C4×D4×C19 ◁ G | |
1380 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)(20,21)(22,23)(24,25)(26,29)(27,28)(30,31)(33,38)(34,42)(35,37)(39,43)(44,45)(46,47);(25,28)(29,31)(32,33)(34,43)(35,40)(36,38)(37,41)(39,44)(42,46)(45,47);(21,23)(24,26,27,30)(25,29,28,31)(32,34,36,45)(33,39,38,46)(35,44,37,42)(40,47,41,43);(25,28)(29,31)(32,35,36,37)(33,40,38,41)(34,44,45,42)(39,47,46,43)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17022);