Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C26×C4 |
| direct product | C19×#20347 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator | C4 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C22×D4 |
| prime radical | C25×C19 | D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C24×C4×C19 ◁ G | |
2270 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)(24,25,26,27)(28,29)(30,38)(31,35)(32,36)(33,37)(34,40)(39,43)(41,42);(21,23)(28,30,32,41,33,39,31,40)(29,34,35,43,37,42,36,38);(30,39)(34,42)(38,43)(40,41);(28,31,33,32)(29,35,37,36)(30,40,39,41)(34,43,42,38)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13335);