Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#69071 |
| Fitting | C3×C5×#346 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×M32 |
| Sylow | C3 ⋊ C4×C5×M32 |
392 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)(14,18)(19,24)(20,25)(26,28);(7,8)(9,10,11,12);(13,14,15,19,16,20,21,26,17,18,22,24,23,25,27,28)600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38279);