Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#1848 |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14,17,20,18,21,16,26)(15,22,24,27,25,28,23,19);(13,15,16,23,18,25,17,24)(14,19,20,22,21,27,26,28);(9,10,11,12)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 580);