Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#32700 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2760 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#2021 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C24×C19 ◁ G | |
778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28,30,25)(23,31,33,26)(24,27)(29,35)(32,34);(20,22)(21,25)(23,32)(24,30)(26,34)(27,28)(29,33)(31,35);(20,23)(21,26)(22,29,30,32)(24,33)(25,34,28,35)(27,31);(25,28)(34,35)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25688);