Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#10587842 |
| Hall | C5×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×#686 |
| Sylow | C5 ⋊ C2×D56 |
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 560 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 405);