Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#10736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C25 | C23×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C4×C19 ◁ G | |
1510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,33,37,40)(31,34)(32,35)(36,39,42,43)(38,41);(21,23)(28,30)(29,33,35,40)(31,36)(32,37)(34,39,41,43)(38,42);(25,27)(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,39,40,43)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3724);