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×#22138 |
| 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 | |
876 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)(32,33,37,41,36,40,35,39)(34,38,43,46,44,42,45,47);(24,25,27,28)(26,29,30,31)(32,33,35,39,36,40,37,41)(34,42,45,46,44,38,43,47);(21,23)(25,28)(29,31)(32,34)(33,38)(35,45)(36,44)(37,43)(39,47)(40,42)(41,46);(24,26,27,30)(25,29,28,31)(32,35,36,37)(33,39,40,41)(34,43,44,45)(38,46,42,47)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15126);