Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×Q8×Dic7 |
| Hall | C5×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ C4×C5×Q8 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 706);