Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#16298 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C26×C19 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
2830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(25,27)(32,33,35,37)(34,38,39,36);(24,25)(26,27)(29,31);(24,25,26,27)(28,29)(30,31)(32,34,35,39)(33,36,37,38);(20,21)(22,23)(24,25)(26,27)(32,33)(34,36)(35,37)(38,39)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 9286);