Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
482 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)(20,21,26,31,27,33,25,32)(22,34,38,52,39,62,37,28)(23,40,44,29,45,55,43,56)(24,30,47,60,48,61,49,59)(35,50,41,53,67,76,66,63)(36,64,69,57,71,78,70,51)(42,58,46,54,72,80,73,81)(65,75,68,79,74,82,83,77);(20,22,25,37,27,39,26,38)(21,28,31,34,33,52,32,62)(23,41,43,35,45,66,44,67)(24,36,47,69,48,71,49,70)(29,53,55,76,56,63,40,50)(30,57,59,64,61,51,60,78)(42,68,46,74,72,83,73,65)(54,77,58,82,81,79,80,75);(20,23,27,45)(21,29,33,56)(22,35,39,67)(24,46,48,73)(25,44,26,43)(28,50,52,76)(30,58,61,80)(31,40,32,55)(34,63,62,53)(36,68,71,83)(37,41,38,66)(42,49,72,47)(51,77,57,79)(54,60,81,59)(64,82,78,75)(65,70,74,69);(20,24)(21,30)(22,36)(23,42)(25,49)(26,47)(27,48)(28,51)(29,54)(31,60)(32,59)(33,61)(34,64)(35,65)(37,70)(38,69)(39,71)(40,58)(41,68)(43,73)(44,46)(45,72)(50,75)(52,57)(53,79)(55,80)(56,81)(62,78)(63,77)(66,83)(67,74)(76,82)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25860);