Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#1308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #95 |
| commutator | C23 | C3×C42×C5 |
| Frattini, cosocle | C2×C42 | C22×C3×C5 |
| prime radical | C23×C3×C5 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,12,17,14,16,13,18)(11,19,20,24,21,15,22,23)(25,26,28,31,29,32,36,39)(27,33,35,40,34,30,37,38);(9,11,13,20,14,21,12,22)(10,15,18,23,16,19,17,24)(25,27)(26,30,32,33)(28,35)(29,34)(31,38,39,40)(36,37)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 40);