Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13175 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13175 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1943 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
256 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)(21,27)(22,31,34,47)(23,25)(24,38)(28,42,44,45)(29,39)(30,36)(32,43,49,51)(33,48,35,46)(37,40);(20,21)(22,32,34,49)(23,36)(24,39)(25,27)(26,30)(28,35,44,33)(29,40)(31,45,47,42)(37,41)(38,50)(43,46,51,48);(20,22,24,31,25,35,38,48,26,34,40,47,23,33,37,46)(21,28,29,43,27,32,41,42,30,44,39,51,36,49,50,45)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6163);