Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#67637 |
| Hall | C3×C5 ⋊ #1390 |
| Sylow | C3 ⋊ C5×#1390 |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(14,17)(18,19);(7,8)(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, 4743);