Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C19 · Schur multiplier (H2) = C22×C8 |
| direct product | C19×#8148 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C19 | C23 |
| commutator | C22 | C2×C4×C8×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C23×C19 | C2×C42 |
| prime radical | C24×C19 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C19 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
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)(24,25,27,30,28,26,29,31)(32,33,36,34,35,38,37,39);(21,23)(32,33,37,39,35,38,36,34);(24,26,27,31,28,25,29,30)(32,34,36,38,35,39,37,33)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1136);