Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of Dic70 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D35 |
| Fitting | C22×C4×C5×C7 ⋊ C2 |
| Hall | C5×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ C4×C22⋊D5 |
| Sylow | C5 ⋊ C4×C22⋊D7 |
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 560 |
292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 864);