Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#24483 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C22⋊C4×C19 ◁ G | |
984 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)(26,30)(27,29)(28,31)(32,33)(34,40)(35,37)(36,39)(38,42)(41,46)(43,45)(44,47);(24,26,27,31)(25,28,29,30)(33,37)(34,41)(36,43)(38,46)(40,47)(42,44);(21,23)(32,34,35,42)(33,38,37,40)(36,44,43,41)(39,46,45,47);(25,29)(28,30)(33,37)(38,40)(39,45)(46,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17471);