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) = C22 |
| direct product | C3×C5×#1493 |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(10,13)(11,15)(14,16)(17,18,21,23,22,19,20,24);(9,10,12,14)(11,16,15,13)(17,19,22,18)(20,23,21,24);(18,19)(23,24)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 225);