Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#442 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(22,31,35,48)(23,37)(24,28)(25,38)(26,30)(27,34,44,51)(29,39)(32,49,43,40)(33,47,36,45)(41,42)(46,50);(20,22)(21,27)(23,32)(24,33)(25,40)(26,35)(28,43)(29,45)(30,44)(31,41)(34,50)(36,37)(38,48)(39,51)(42,49)(46,47);(20,23,37,21,26,28,24,30)(22,32,36,27,35,43,33,44)(25,41,50,46,42,38,39,29)(31,34,47,49,48,51,45,40);(20,24,26,37)(21,28,30,23)(22,33,35,36)(25,39,42,50)(27,43,44,32)(29,41,46,38)(31,47,48,45)(34,40,51,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26459);