Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2082 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C23×C3×C5 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
368 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,14,19,15,20,13,18)(11,21,24,16,25,32,23,33)(12,26,28,34,29,35,30,17)(22,37,38,40,27,31,39,36);(9,11,15,25)(10,16,20,33)(12,27,29,22)(13,24,14,23)(17,31,34,37)(18,32,19,21)(26,40,35,36)(28,38,30,39);(9,12,13,28,15,29,14,30)(10,17,18,26,20,34,19,35)(11,22,23,38,25,27,24,39)(16,31,21,36,33,37,32,40)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 814);