Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
994 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)(20,21,25,30)(22,32,35,48)(23,29,24,39)(26,31,42,47)(27,40,45,33)(28,41,37,38)(34,43,36,50)(44,49,46,51);(20,22,25,35)(21,27,30,45)(23,33,24,40)(26,36,42,34)(28,43,37,50)(29,48,39,32)(31,46,47,44)(38,49,41,51);(20,21)(22,27)(23,37)(24,28)(25,30)(26,31)(29,41)(32,49)(33,50)(34,44)(35,45)(36,46)(38,39)(40,43)(42,47)(48,51);(20,23,25,24)(21,28,30,37)(22,33,35,40)(26,38,42,41)(27,43,45,50)(29,47,39,31)(32,46,48,44)(34,51,36,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11409);