Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33588 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
680 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)(21,23)(24,25,30,35)(26,31,37,52)(27,40,43,74)(28,44,48,73)(29,49,46,34)(32,55,57,41)(33,58,60,47)(36,62,63,85)(38,68,66,84)(39,71,67,54)(42,75,50,59)(45,61,76,56)(51,77,78,64)(53,81,80,70)(65,86,72,82)(69,83,87,79);(20,21,22,23)(24,26)(25,31)(27,36)(28,38)(29,39)(30,37)(32,51)(33,53)(34,54)(35,52)(40,62)(41,64)(42,65)(43,63)(44,68)(45,69)(46,67)(47,70)(48,66)(49,71)(50,72)(55,77)(56,79)(57,78)(58,81)(59,82)(60,80)(61,83)(73,84)(74,85)(75,86)(76,87);(24,27,30,43)(25,32,35,57)(26,36,37,63)(28,45,48,76)(29,50,46,42)(31,51,52,78)(33,59,60,75)(34,61,49,56)(38,69,66,87)(39,72,67,65)(40,73,74,44)(41,58,55,47)(53,82,80,86)(54,83,71,79)(62,84,85,68)(64,81,77,70);(26,37)(31,52)(36,63)(38,66)(39,67)(51,78)(53,80)(54,71)(62,85)(64,77)(65,72)(68,84)(69,87)(70,81)(79,83)(82,86)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26576);