Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×#69102 |
| Fitting | C3×C5×C22⋊C16 ⋊ C2 |
| Hall | C3×C5 ⋊ #2168 |
| Sylow | C3 ⋊ C5×#2168 |
328 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)(7,8)(13,15,16,23,17,21,22,28,18,24,25,27,26,14,19,20);(6,7,8)(10,12);(9,10)(11,12)(13,14,16,20,17,15,22,23,18,21,25,28,26,24,19,27)480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 40724);