Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#2249 ⋊ C2 |
| Sylow | C7 ⋊ #13691 |
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|b^2=d,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=ef,f^a=fg,g^a=gh,e^c=ef,f^c=fg,g^c=gh,i^c=i^6151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 90379);