Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×D7×Q16 |
| Fitting | C7×Q8×Q16 ⋊ C2 |
| Sylow | C7 ⋊ C2×Q8×Q16 |
1830 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1050013);