Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33531 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3584 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
1090 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)(20,21,26,31)(22,32,35,61)(23,28,37,52)(24,40,45,75)(25,46,43,30)(27,48,50,34)(29,55,58,44)(33,62,63,60)(36,67,47,56)(38,69,42,74)(39,72,68,54)(41,59,77,51)(49,66,79,64)(53,78,57,71)(65,83,73,81)(70,82,76,80);(20,22)(21,27)(23,33)(24,41)(25,47)(26,35)(28,49)(29,56)(30,59)(31,50)(32,40)(34,44)(36,43)(37,63)(38,70)(39,73)(42,76)(45,77)(46,51)(48,55)(52,79)(53,81)(54,82)(57,83)(58,67)(60,74)(61,75)(62,69)(64,71)(65,68)(66,78)(72,80);(20,23)(21,28)(22,33)(24,42)(25,39)(26,37)(27,49)(29,57)(30,54)(31,52)(32,60)(34,66)(35,63)(36,65)(38,45)(40,74)(41,76)(43,68)(44,78)(46,72)(47,73)(48,64)(50,79)(51,80)(53,58)(55,71)(56,83)(59,82)(61,62)(67,81)(69,75)(70,77);(23,37)(28,52)(33,63)(38,42)(39,68)(49,79)(53,57)(54,72)(60,62)(64,66)(65,73)(69,74)(70,76)(71,78)(80,82)(81,83)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26520);