Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#4039 |
| Fitting | C5×C7×C4⋊C4 ⋊ C2 |
| Hall | C5×C7 ⋊ C4×D4 |
| Sylow | C5 ⋊ C4×C7×D4 |
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 560 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5,6,7)(8,9,11,12,10)(13,14,15,16)(18,20);(17,18,19,20);(9,10)(11,12)(18,20)280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 744);