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×#23091 |
| 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 | |
892 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)(25,29)(30,31)(32,33,37,39,36,40,35,44)(34,38,42,47,43,41,45,46);(24,25,28,29)(26,30,27,31)(32,33,35,44,36,40,37,39)(34,41,45,47,43,38,42,46);(21,23)(24,26,28,27)(25,30,29,31)(32,34,36,43)(33,38,40,41)(35,45,37,42)(39,47,44,46);(24,27,28,26)(25,30,29,31)(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, 16079);