Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2540 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C4×D4×C19 ◁ G | |
918 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)(26,30)(27,28)(29,31)(32,33)(34,40)(35,38)(36,39)(37,42)(41,46)(43,45)(44,47);(20,21,23,22)(25,28)(29,30)(32,34,35,42)(33,37,38,40)(36,41,44,43)(39,45,47,46);(20,21,23,22)(34,41)(36,44)(37,45)(39,47)(40,46)(42,43);(20,22,23,21)(24,26,27,31)(25,29,28,30)(33,38)(37,40)(39,47)(45,46)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19227);