Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13269 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #391 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1985 |
| prime radical | C23×C19 | C2×M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
308 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)(20,21,26,22,25,30,43,34,27,31,44,35,24,29,42,33)(23,36,39,48,38,28,45,32,40,46,50,37,41,47,51,49);(20,22,26,29,25,34,43,21,27,35,44,30,24,33,42,31)(23,37,50,47,38,49,51,36,40,48,39,28,41,32,45,46);(20,23,25,38,27,40,24,41)(21,28,29,36,31,47,30,46)(22,32,33,48,35,49,34,37)(26,39,43,45,44,50,42,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6257);