Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#12663 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C19 | C23 |
| commutator | C22 | C2×C4×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle, prime radical | C23×C19 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C19 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(28,29,31,35,32,30,37,38,33,36,40,43,41,39,34,42);(21,23)(24,25,26,27);(28,30,31,38,32,36,37,43,33,39,40,42,41,29,34,35)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5651);