Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26367 |
| 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 | |
804 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)(20,21)(22,23)(24,25,28,30)(26,29,27,31)(32,33)(34,38)(35,40)(36,39)(37,41)(42,47)(43,45)(44,46);(21,23)(24,26,28,27)(25,29,30,31)(32,34)(33,38)(35,43)(36,44)(37,42)(39,46)(40,45)(41,47);(24,27,28,26)(25,29,30,31)(33,39)(34,42)(35,37)(38,45)(43,44)(46,47);(21,23)(32,35,36,37)(33,40,39,41)(34,43,44,42)(38,45,46,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19355);