Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#24988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#472 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
656 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)(21,26)(22,30)(23,35)(24,36)(28,43)(29,40)(33,34)(37,48)(38,42)(41,49)(44,46)(45,51);(20,21,24,26,25,29,36,40)(22,31,30,38,34,27,33,42)(23,28,35,39,37,43,48,50)(32,45,44,49,47,41,46,51);(20,22)(21,27)(23,32)(24,33)(25,34)(26,38)(28,41)(29,31)(30,36)(35,46)(37,47)(39,49)(40,42)(43,45)(44,48)(50,51);(20,23,36,48,25,37,24,35)(21,28,40,50,29,43,26,39)(22,32,30,44,34,47,33,46)(27,41,42,51,31,45,38,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17976);