Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#6503 |
| Fitting | C2×C5×C7×D4 ⋊ C2 |
| Hall | C5×C7 ⋊ #127 |
| Sylow | C7 ⋊ C5×#127 |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 560 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(14,16)(18,20);(17,18,19,20);(7,8)(9,10)(11,12)(13,14)(15,16)(18,20)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 697);