Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#22142 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C19×#392 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
882 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)(25,28)(26,30)(32,33,37,39,36,40,35,44)(34,38,42,47,43,41,45,46);(24,25,27,28)(26,29,30,31)(32,33,35,44,36,40,37,39)(34,41,45,47,43,38,42,46);(21,23)(25,28)(29,31)(32,34)(33,38)(35,45)(36,43)(37,42)(39,47)(40,41)(44,46);(24,26,27,30)(25,29,28,31)(32,35,36,37)(33,39,40,44)(34,42,43,45)(38,46,41,47)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15130);