Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
406 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)(21,27)(22,31)(23,25)(24,38)(28,44)(29,39)(30,36)(32,47)(33,40)(34,49)(35,48)(37,41)(42,46)(45,50);(20,21)(22,32)(23,36)(24,39)(25,27)(26,30)(28,34)(29,41)(31,46)(33,45)(35,42)(37,43)(38,51)(40,47)(44,48)(49,50);(20,22)(21,28,30,32)(23,35)(24,40)(25,33)(26,34)(27,42,36,45)(29,47,39,44)(31,38)(37,49)(41,48)(43,46,51,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6392);