Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×(C22⋊D7)⋊C4 |
| unambiguous semidirect product | (C22⋊D7)⋊(C4×C5) |
| Fitting | C5×C7×C22⋊C4 ⋊ C2 |
| Hall | C5×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ C4×C5×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)(6,7,9,11,12,10,8)(13,14,15,16)(18,20);(17,18)(19,20);(7,8)(9,10)(11,12)(18,20)250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 646);