Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#22460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#578 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1286 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)(20,21,26,31,27,32,25,45)(22,33,36,28,37,52,46,51)(23,38,40,54,41,29,48,55)(24,30,43,59,44,58,47,57)(34,62,65,49,66,60,64,69)(35,61,67,50,68,56,42,75)(39,70,73,79,74,53,72,78)(63,77,71,76,81,80,82,83);(20,22)(21,28)(23,34)(24,42)(25,46)(26,36)(27,37)(29,49)(30,56)(31,52)(32,51)(33,45)(35,43)(38,69)(39,71)(40,65)(41,66)(44,67)(47,68)(48,64)(50,57)(53,77)(54,62)(55,60)(58,61)(59,75)(63,72)(70,80)(73,81)(74,82)(76,78)(79,83);(20,23,27,41)(21,29,32,38)(22,34,37,66)(24,39,44,74)(25,40,26,48)(28,49,51,69)(30,53,58,70)(31,54,45,55)(33,60,52,62)(35,63,68,81)(36,64,46,65)(42,71,67,82)(43,72,47,73)(50,76,75,83)(56,77,61,80)(57,78,59,79);(20,24)(21,30)(22,35)(23,39)(25,47)(26,43)(27,44)(28,50)(29,53)(31,59)(32,58)(33,61)(34,63)(36,67)(37,68)(38,70)(40,73)(41,74)(42,46)(45,57)(48,72)(49,76)(51,75)(52,56)(54,79)(55,78)(60,80)(62,77)(64,82)(65,71)(66,81)(69,83)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15448);