Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26809 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C22⋊C4×C19 ◁ G | |
776 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(24,25)(26,31)(27,29)(28,30)(32,33,37,41)(34,38,44,47)(35,39,36,40)(42,45,43,46);(20,21,23,22)(24,26,28,27)(25,29,30,31)(32,34)(33,38)(35,43)(36,42)(37,44)(39,46)(40,45)(41,47);(20,21,23,22)(24,27,28,26)(25,29,30,31)(34,42)(35,36)(38,45)(39,40)(43,44)(46,47);(20,22,23,21)(25,30)(29,31)(32,35,37,36)(33,39,41,40)(34,43,44,42)(38,46,47,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19797);