Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#4013 |
| Hall | C5×C7 ⋊ #100 |
| Sylow | C5 ⋊ C7×#100 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5,6,7)(8,9,10,12,11)(14,17)(15,19);(9,10,11,12)(13,14,15,18,16,17,19,20)133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 271);