Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24810 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
810 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)(20,21,25,48,27,32,26,31)(22,33,36,28,38,52,37,53)(23,39,49,29,43,56,42,57)(24,44,45,30,47,72,46,58)(34,50,40,54,62,76,61,75)(35,63,64,59,66,51,65,77)(41,55,73,71,70,79,69,67)(60,78,68,82,81,83,80,74);(20,22,25,36,27,38,26,37)(21,28,31,33,32,53,48,52)(23,40,42,34,43,61,49,62)(24,35,45,64,47,66,46,65)(29,54,56,76,57,75,39,50)(30,51,44,59,58,63,72,77)(41,68,69,60,70,80,73,81)(55,78,71,82,79,83,67,74);(20,23)(21,29)(22,34)(24,41)(25,42)(26,49)(27,43)(28,50)(30,55)(31,56)(32,57)(33,54)(35,60)(36,61)(37,40)(38,62)(39,48)(44,71)(45,69)(46,73)(47,70)(51,74)(52,75)(53,76)(58,79)(59,78)(63,82)(64,80)(65,68)(66,81)(67,72)(77,83);(20,24,26,46,27,47,25,45)(21,30,48,72,32,58,31,44)(22,35,37,65,38,66,36,64)(23,41,49,73,43,70,42,69)(28,51,52,77,53,63,33,59)(29,55,39,67,57,79,56,71)(34,60,40,68,62,81,61,80)(50,74,75,83,76,82,54,78)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17798);