Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1898 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C19×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×C19×2−1+4 ◁ G | |
646 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)(20,21,26,31,27,32,25,30)(22,24,29,42,35,43,44,33)(23,36,39,28,40,46,38,47)(34,49,45,37,50,51,48,41);(20,22,33,21)(23,34,49,28)(24,31,25,44)(26,29,43,30)(27,35,42,32)(36,39,45,41)(37,46,38,48)(40,50,51,47);(20,23,27,40)(21,28,32,47)(22,34,35,50)(24,41,43,37)(25,39,26,38)(29,48,44,45)(30,46,31,36)(33,49,42,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6091);