Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24423 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1284 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)(20,21,27,49,26,31,25,32)(22,33,47,52,37,28,36,58)(23,38,48,29,41,59,42,55)(24,43,45,56,46,30,44,57)(34,62,68,60,64,53,39,50)(35,51,66,77,67,61,65,76)(40,69,73,74,71,79,72,54)(63,81,70,75,82,78,83,80);(20,22,26,37)(21,28,31,33)(23,39,41,68)(24,35,46,67)(25,47,27,36)(29,53,55,62)(30,51,43,61)(32,58,49,52)(34,48,64,42)(38,50,59,60)(40,70,71,83)(44,66,45,65)(54,78,74,81)(56,77,57,76)(63,72,82,73)(69,75,79,80);(20,23)(21,29)(22,34)(24,40)(25,48)(26,41)(27,42)(28,50)(30,54)(31,55)(32,59)(33,60)(35,63)(36,68)(37,64)(38,49)(39,47)(43,74)(44,73)(45,72)(46,71)(51,75)(52,62)(53,58)(56,69)(57,79)(61,80)(65,70)(66,83)(67,82)(76,78)(77,81);(20,24)(21,30)(22,35)(23,40)(25,45)(26,46)(27,44)(28,51)(29,54)(31,43)(32,57)(33,61)(34,63)(36,66)(37,67)(38,69)(39,70)(41,71)(42,73)(47,65)(48,72)(49,56)(50,75)(52,77)(53,78)(55,74)(58,76)(59,79)(60,80)(62,81)(64,82)(68,83)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17411);