Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13021 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1879 |
| prime radical | C19×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
462 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)(20,21,26,33,27,34,50,65,28,35,25,32,49,64,24,31)(22,36,39,58,40,63,38,68,41,66,48,29,53,56,51,57)(23,42,45,69,46,67,43,30,47,60,44,61,54,59,52,62)(37,71,73,78,74,55,79,80,75,81,76,83,77,82,72,70);(20,22,27,53,28,41,49,40)(21,29,34,68,35,58,64,57)(23,37,54,74,47,75,46,77)(24,48,26,38,50,39,25,51)(30,55,69,81,62,82,61,71)(31,63,33,36,65,56,32,66)(42,78,59,80,60,83,67,70)(43,73,45,79,52,76,44,72);(20,23)(21,30)(22,37)(24,45)(25,43)(26,52)(27,54)(28,47)(29,55)(31,60)(32,59)(33,67)(34,69)(35,62)(36,70)(38,76)(39,72)(40,77)(41,75)(42,65)(44,50)(46,49)(48,79)(51,73)(53,74)(56,78)(57,71)(58,82)(61,64)(63,83)(66,80)(68,81)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6009);