Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23801 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C43×C19 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
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)(24,25,27,28)(26,29,30,31)(32,33,36,40,37,41,46,47)(34,42,43,39,35,44,45,38);(20,21)(22,23)(25,28)(29,31)(32,34,37,35)(33,38,41,39)(36,45,46,43)(40,44,47,42);(21,23)(32,35,37,34)(33,39,41,38)(36,43,46,45)(40,42,47,44);(24,26,27,30)(25,29,28,31)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16789);