Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11006 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C2×C19×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
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)(24,25)(26,34,37,39)(27,30)(28,32)(29,33)(31,36,38,35);(20,21)(22,23)(25,30)(27,28)(31,34)(32,33)(35,36)(38,39);(21,23)(24,26)(25,31)(27,36)(28,35)(29,37)(30,34)(32,39)(33,38)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3994);