Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#78628 |
| Fitting | C3×C5×#407 ⋊ C2 |
| Hall | C3×C5 ⋊ D4×M16 |
| Sylow | C3 ⋊ C5×D4×M16 |
1088 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4,5)(6,7,8)(14,15)(19,20);(7,8)(13,15,16,20,17,14,18,19);(10,12);(9,10)(11,12)(13,14,16,19,17,15,18,20)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 141367);