Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#32952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1266 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)(22,34,39,50)(23,40,43,56)(24,30,45,55)(25,32,26,31)(28,38,51,37)(29,46,53,42)(35,60,63,48)(36,59,65,76)(41,69,72,68)(44,57,47,54)(49,67,74,64)(52,70,77,71)(58,66,75,62)(61,73,82,79)(78,80,83,81);(20,22,26,38,27,39,25,37)(21,28,32,50,33,51,31,34)(23,35,46,66,43,63,42,62)(24,36,47,67,45,65,44,64)(29,48,56,75,53,60,40,58)(30,49,57,76,55,74,54,59)(41,61,71,81,72,82,70,80)(52,73,69,83,77,79,68,78);(20,23)(21,29)(22,35)(24,41)(25,42)(26,46)(27,43)(28,48)(30,52)(31,40)(32,56)(33,53)(34,58)(36,61)(37,62)(38,66)(39,63)(44,70)(45,72)(47,71)(49,73)(50,75)(51,60)(54,68)(55,77)(57,69)(59,78)(64,80)(65,82)(67,81)(74,79)(76,83);(20,24)(21,30)(22,36)(23,41)(25,44)(26,47)(27,45)(28,49)(29,52)(31,54)(32,57)(33,55)(34,59)(35,61)(37,64)(38,67)(39,65)(40,68)(42,70)(43,72)(46,71)(48,73)(50,76)(51,74)(53,77)(56,69)(58,78)(60,79)(62,80)(63,82)(66,81)(75,83)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25940);