Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×#86037 |
| Fitting | C3×C5×#525 ⋊ C2 |
| Hall | C3×C5 ⋊ D4×#41 |
| Sylow | C3 ⋊ C5×D4×#41 |
3296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 5 generators on 20 points:
(1,2,3,4,5)(6,7,8)(13,15,16,19)(14,18,17,20);(14,17)(18,20);(10,12);(7,8)(13,14)(15,18)(16,17)(19,20);(7,8)(9,10)(11,12)(14,17)(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, 208731);