Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#68955 |
| Hall | C3×C5 ⋊ #1996 |
| Sylow | C3 ⋊ C5×#1996 |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(7,8)(17,19,20,24)(18,21,22,23);(6,7,8)(9,11)(10,13,14,16)(12,15);(9,10)(11,13,15,16)(12,14)(17,18,20,22)(19,23,24,21)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 33172);