Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C29 |
| direct product | C19×#34070 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C2×C19×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
3102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,27,26)(28,29)(30,36)(31,35)(32,34)(33,37)(38,42)(39,41)(40,43);(24,26,27,25)(28,30)(29,33)(31,38)(32,37)(34,36)(35,40)(39,43)(41,42);(20,21,22,23)(30,37)(33,36)(38,43)(40,42);(29,34)(33,36)(35,41)(40,42);(28,31,32,39)(29,35,34,41)(30,38,37,43)(33,40,36,42)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27058);