Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9239 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,26,29)(22,25,28,24)(23,30)(27,31)(32,34)(33,35)(36,37,40,45,41,44,39,43)(38,42,46,49,47,50,48,51);(20,22,24,21,26,28,25,29)(23,30,32,27,33,35,31,34)(36,38,39,46,41,47,40,48)(37,42,45,51,44,50,43,49);(20,23)(21,27)(22,30)(24,32)(25,31)(26,33)(28,35)(29,34)(36,39,41,40)(37,43,44,45)(38,46,47,48)(42,49,50,51)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2238);