Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C42 |
| direct product | C19×#21985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
806 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)(34,41)(35,43)(36,40)(37,38)(39,44)(42,47)(45,46);(24,25)(26,29)(27,28)(30,31)(32,34,36,37)(33,38,40,41)(35,44,45,42)(39,43,47,46);(25,28)(29,31)(32,35,37,44,36,45,34,42)(33,39,41,43,40,47,38,46);(24,26,27,30)(25,29,28,31)(33,40)(38,41)(39,47)(43,46)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14973);