Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36608 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
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)(20,21,25,23)(22,26,24,27)(29,33)(34,35)(37,41)(42,43);(20,21,25,23)(22,27,24,26)(28,29)(30,34)(31,35)(32,33)(36,37,40,41)(38,42,39,43);(20,22,25,24)(21,26,23,27)(28,29)(30,34)(31,35)(32,33)(36,38,40,39)(37,42,41,43);(20,23,25,21)(22,26,24,27)(28,30,32,31)(29,34,33,35);(20,24,25,22)(21,27,23,26)(28,31,32,30)(29,35,33,34)(36,39,40,38)(37,43,41,42)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29596);