Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1961 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,33)(23,39,43,72)(24,45)(25,31)(26,49)(27,32)(28,36)(29,42,57,44)(30,46)(34,58)(35,65,67,81)(37,60)(38,62)(40,73,76,59)(41,77,78,56)(47,50)(48,61)(51,75,70,82)(52,68)(53,63)(54,69)(55,66,80,83)(64,79,74,71);(20,22,34,63,26,37,24,36,27,38,46,68,25,48,47,69)(21,28,50,60,31,53,30,33,32,54,45,61,49,52,58,62)(23,40,74,83,44,67,78,82,43,76,64,66,42,35,41,75)(29,55,71,73,39,70,77,65,57,80,79,59,72,51,56,81);(20,23)(21,29,32,57)(22,35,38,67)(24,41)(25,42)(26,44)(27,43)(28,51)(30,56,58,77)(31,39,49,72)(33,59)(34,64)(36,66,69,83)(37,40,48,76)(45,71,50,79)(46,74)(47,78)(52,80)(53,55)(54,70)(60,65)(61,81)(62,73)(63,82,68,75)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6204);