Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#83502 |
| Fitting | C3×C5×#546 ⋊ C2 |
| Hall | C3×C5 ⋊ #3264 |
| Sylow | C3 ⋊ C5×#3264 |
1136 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)(14,18)(15,20)(17,19);(10,12);(13,14)(15,18)(16,19)(17,20);(7,8)(9,10)(11,12)(14,17)(15,20)(18,19)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 178894);