Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×D8×C19 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C19 | D4 |
| commutator | C4 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C22×D4 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C19 ◁ C43×C19 ◁ G | |
1350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(5,6,7,8);(9,10,11,12,13,14,15,16);(10,16)(11,15)(12,14)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13485);