Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×C22⋊#401 |
| unambiguous semidirect product | C22⋊(C19×#401) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1650 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)(21,23)(24,25,27,29)(26,28,30,31)(32,33,36,37)(34,39,38,35)(40,41)(42,45)(43,47)(44,46);(26,30)(28,31)(33,37)(34,38)(40,42,44,47)(41,45,46,43);(24,26)(25,28)(27,30)(29,31)(32,34,36,38)(33,35,37,39)(40,42)(41,43)(44,47)(45,46);(20,21)(22,23)(24,25)(26,28)(27,29)(30,31)(32,35)(33,38)(34,37)(36,39)(40,43)(41,42)(44,45)(46,47)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 7815);