Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#578 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
1086 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,30,35)(26,36,40,64)(27,32,41,55)(28,44,48,62)(29,49,46,34)(31,51,54,38)(33,58,60,47)(37,63,65,85)(39,68,50,59)(42,71,69,84)(43,74,70,57)(45,61,76,53)(52,77,78,66)(56,81,80,73)(67,86,75,82)(72,83,87,79);(24,26,30,40)(25,31,35,54)(27,37,41,65)(28,45,48,76)(29,50,46,39)(32,52,55,78)(33,59,60,68)(34,61,49,53)(36,62,64,44)(38,58,51,47)(42,72,69,87)(43,75,70,67)(56,82,80,86)(57,83,74,79)(63,84,85,71)(66,81,77,73);(21,23)(24,27)(25,32)(26,37)(28,42)(29,43)(30,41)(31,52)(33,56)(34,57)(35,55)(36,63)(38,66)(39,67)(40,65)(44,71)(45,72)(46,70)(47,73)(48,69)(49,74)(50,75)(51,77)(53,79)(54,78)(58,81)(59,82)(60,80)(61,83)(62,84)(64,85)(68,86)(76,87);(27,41)(32,55)(37,65)(42,69)(43,70)(52,78)(56,80)(57,74)(63,85)(66,77)(67,75)(71,84)(72,87)(73,81)(79,83)(82,86)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26513);