Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33596 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,27,33)(22,34,36,53)(23,40,43,73)(24,32,26,30)(25,45,48,57)(28,39,51,37)(29,54,56,42)(31,44,59,47)(35,63,64,83)(38,52,67,79)(41,74,49,58)(46,60,76,55)(50,77,78,69)(61,81,80,66)(62,68,75,70)(65,72,71,82);(20,22,24,37,27,36,26,39)(21,28,30,34,33,51,32,53)(23,35,41,65,43,64,49,71)(25,38,44,68,48,67,47,70)(29,50,55,61,56,78,60,80)(31,52,57,62,59,79,45,75)(40,72,58,63,73,82,74,83)(42,66,46,69,54,81,76,77);(20,23)(21,29)(22,35)(24,41)(25,46)(26,49)(27,43)(28,50)(30,55)(31,58)(32,60)(33,56)(34,61)(36,64)(37,65)(38,69)(39,71)(40,45)(42,47)(44,54)(48,76)(51,78)(52,63)(53,80)(57,73)(59,74)(62,82)(66,70)(67,77)(68,81)(72,75)(79,83);(22,36)(28,51)(34,53)(35,64)(37,39)(38,67)(50,78)(52,79)(61,80)(62,75)(63,83)(65,71)(66,81)(68,70)(69,77)(72,82)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26584);