Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13259 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #459 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1982 |
| prime radical | C19×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
472 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)(20,21,25,32,26,31,41,50,27,33,40,29,24,42,23,30)(22,34,38,48,37,49,36,45,39,44,35,28,43,46,51,47);(20,22,26,43,27,39,24,37)(21,28,31,45,33,48,42,47)(23,35,25,36,41,38,40,51)(29,44,30,49,32,34,50,46);(20,23,24,40,27,41,26,25)(21,29,31,30,33,32,42,50)(22,35,37,51,39,38,43,36)(28,44,45,49,48,34,47,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6247);