Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
460 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 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)(24,25,30,37,54,70,55,36,32,39,28,35,31,38,29,56)(26,40,44,63,58,61,43,33,46,62,42,72,45,69,57,64)(27,47,50,68,59,65,53,67,52,71,48,34,51,66,49,73)(41,75,78,74,82,87,77,83,80,86,76,84,79,60,81,85);(20,21,22,23)(24,26)(25,33)(27,41)(28,43)(29,44)(30,57)(31,58)(32,46)(34,60)(35,69)(36,40)(37,61)(38,72)(39,64)(42,55)(45,54)(47,83)(48,77)(49,78)(50,81)(51,82)(52,80)(53,76)(56,62)(59,79)(63,70)(65,74)(66,84)(67,75)(68,87)(71,85)(73,86);(24,27,32,52)(25,34,39,68)(26,41,46,80)(28,53,30,49)(29,50,55,48)(31,59,54,51)(33,60,64,87)(35,47,37,71)(36,65,56,66)(38,73,70,67)(40,74,62,84)(42,77,44,81)(43,76,57,78)(45,82,58,79)(61,85,69,83)(63,75,72,86)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6008);