Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#68730 |
| Hall | C3×C5 ⋊ #1986 |
| Sylow | C3 ⋊ C5×#1986 |
520 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)(9,11,12,16)(10,13,14,15);(6,7,8)(17,18,19,23,20,22,24,21);(9,10,12,14)(11,15,16,13)(18,21,22,23)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 32818);