Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6512 |
| Fitting | C5×C7×#41 ⋊ C2 |
| Hall | C5×C7 ⋊ AGL(1,ℤ/8) |
| Sylow | C7 ⋊ C5×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(13,14)(15,20)(16,18)(17,19);(14,18)(17,20);(7,8)(9,10)(11,12)(14,17)(15,19)(18,20)205 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#6512⋊C3, D5×#6512, C5×D7×AGL(1,ℤ/8), … |
| maximal normal subgroup of | C5×#6512⋊C3, D5×#6512, C5×D7×AGL(1,ℤ/8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 713);