Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13322 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
520 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)(24,25,31,37)(26,38,43,69)(27,44,47,66)(28,48,53,64)(29,36,30,35)(32,55,59,40)(33,54,61,46)(34,51,65,52)(39,70,73,87)(41,62,42,68)(45,63,50,60)(49,57,75,58)(56,79,86,82)(67,76,84,72)(71,77,74,85)(78,83,81,80);(20,21)(22,23)(24,26,31,43)(25,32,37,59)(27,39,47,73)(28,49,53,75)(29,42,30,41)(33,56,61,86)(34,62,65,68)(35,58,36,57)(38,64,69,48)(40,51,55,52)(44,77,66,85)(45,79,50,82)(46,76,54,72)(60,87,63,70)(67,78,84,81)(71,83,74,80);(21,23)(24,27)(25,33)(26,39)(28,50)(29,54)(30,46)(31,47)(32,56)(34,63)(35,66)(36,44)(37,61)(38,67)(40,74)(41,76)(42,72)(43,73)(45,53)(48,81)(49,82)(51,80)(52,83)(55,71)(57,77)(58,85)(59,86)(60,65)(62,70)(64,78)(68,87)(69,84)(75,79)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6310);