Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11280 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #393 |
| commutator | C24 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1442 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,24,29,25,28,39,45)(22,30,33,46,32,26,38,41)(23,34,37,48,36,27,42,44)(31,40,47,50,35,43,49,51);(20,22)(21,26)(23,35,36,31)(24,38)(25,32)(27,43,34,40)(28,30)(29,46)(33,39)(37,47,42,49)(41,45)(44,50,48,51);(20,23)(21,27,28,34)(22,31)(24,37)(25,36)(26,40,30,43)(29,44,45,48)(32,35)(33,47)(38,49)(39,42)(41,50,46,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4268);