Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#8403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #120 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C2×C19×#534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
1364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 39 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)(26,27,30,31)(28,29)(32,33,35,37,36,39,34,38);(21,23)(24,26)(25,27)(28,30)(29,31)(33,37)(34,35)(38,39);(24,27)(25,26)(28,31)(29,30)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1391);