Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#8149 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C19 | C23 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C23×C19 | C2×C42 |
| prime radical | C24×C19 | C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C19 ◁ G | |
554 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)(24,25,28,30,27,26,29,31)(32,33,35,34,36,37,39,38);(21,23)(25,26)(30,31)(32,33,35,34,36,37,39,38);(24,26,28,31,27,25,29,30)(32,34,35,37,36,38,39,33)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1137);