Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21782 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1382 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)(22,29,31,25)(23,28)(24,27)(26,30,35,32)(33,34);(20,22)(21,25)(23,32)(24,31)(26,34)(27,29)(28,35)(30,33);(20,22)(21,26)(23,32)(24,31)(25,28)(27,35)(29,34)(30,33);(20,22)(21,25)(23,30)(24,31)(26,28)(27,29)(32,33)(34,35)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14770);