Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×Q8×D5 |
| Fitting | C2×C5×C7×Q8 ⋊ C2 |
| Hall | C5×C7 ⋊ C22×Q8 |
| Sylow | C5 ⋊ C22×C7×Q8 |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1049);