Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#68962 |
| Fitting | C3×C5×#342 ⋊ C2 |
| Hall | C3×C5 ⋊ #1889 |
| Sylow | C3 ⋊ C5×#1889 |
1156 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)(6,7)(13,15)(14,17)(16,20)(18,19);(9,11,12,10)(13,14)(15,17)(16,18)(19,20);(7,8)(9,10,12,11)(13,14)(15,19,20,17)(16,18)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 27313);