Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8626 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#8641 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #380 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #117 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,28,26,23,24,34)(22,29,32,30,33,35,31,27)(37,41)(38,45)(39,42)(44,49)(46,47)(48,50);(20,22,24,31,26,33,25,32)(21,27,28,29,23,30,34,35)(36,37,42,49,40,44,39,41)(38,43,45,50,47,51,46,48);(20,23)(21,26)(22,30)(24,34)(25,28)(27,33)(29,32)(31,35)(36,38,40,47)(37,43,44,51)(39,46,42,45)(41,48,49,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1629);