Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#34595 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27)(22,26,23,25)(28,29,32,35)(30,34,31,33)(36,37)(38,40)(39,41)(42,43);(20,22,24,23)(21,25,27,26)(28,30,32,31)(29,33,35,34)(36,38)(37,40)(39,42)(41,43);(20,22,24,23)(21,26,27,25)(28,31,32,30)(29,34,35,33)(38,42)(40,43);(37,41)(40,43);(20,23,24,22)(21,25,27,26)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27583);