Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | (C22⋊D7)⋊#95 |
| Fitting | C7×C22⋊#95 ⋊ C2 |
| Sylow | C7 ⋊ D4×#95 |
3562 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=h,d^2=g,b^a=be,c^a=cf,d^b=de,i^d=i^6268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 91035);