Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#70079 |
| Fitting | C2×C3×C5×#100 ⋊ C2 |
| Hall | C3×C5 ⋊ #1783 |
| Sylow | C3 ⋊ C5×#1783 |
1640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(7,8)(10,12);(6,7,8)(14,17)(15,19);(9,10)(11,12)(13,14,15,18,16,17,19,20)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 22585);