Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#22410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#548 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×D4×C19 ◁ G | |
1404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,28,33,29,32,26,30)(27,35,34,39,36,31,37,38);(20,21)(22,23)(24,26,29,28)(25,30,32,33)(27,34,36,37)(31,38,35,39);(24,27,29,36)(25,31,32,35)(26,34,28,37)(30,38,33,39);(21,23)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15398);