Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27 |
| direct product | C5×#74878 |
| Fitting | C3×C5×#386 ⋊ C2 |
| Hall | C3×C5 ⋊ D4×C22⋊C4 |
| Sylow | C3 ⋊ C5×D4×C22⋊C4 |
2504 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)(18,20);(7,8)(14,16);(7,8)(17,18)(19,20);(9,10,11,12)(13,14)(15,16)(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, 51596);