Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C8×C19×#124 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C19 | C23 |
| commutator | C22 | C23×C8×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C19 ◁ G | |
974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(10,11)(15,19)(17,20);(9,10,12,11)(13,14,16,18)(15,17,19,20);(9,11,12,10)(13,15)(14,17)(16,19)(18,20)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14618);