Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#20385 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C19 | C23 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C25×C19 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C19 ◁ G | |
1774 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(28,29,32,36,33,31,35,40)(30,34,39,42,38,37,41,43);(21,23)(24,25,26,27)(28,30)(29,34)(31,37)(32,39)(33,38)(35,41)(36,42)(40,43);(28,31,32,40,33,29,35,36)(30,37,39,43,38,34,41,42);(30,38)(34,37)(39,41)(42,43)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13373);