Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C5×#83937 |
| Fitting | C2×C3×C5×AGL(1,ℤ/8) ⋊ C2 |
| Hall | C3×C5 ⋊ #3151 |
| Sylow | C3 ⋊ C5×#3151 |
1312 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)(14,18)(17,20);(7,8)(9,10,11,12);(13,14,15,17,16,18,19,20);(10,12)(14,17)(15,19)(18,20)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 164824);