Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#1857 ⋊ C2 |
| Sylow | C7 ⋊ #13427 |
462 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 75 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|a^2=h,c^2=d,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,i^a=i^6,c^b=cf,e^b=eg,f^b=fh,i^b=i^6,e^c=eh,f^c=fh,g^c=gh,f^e=fh127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 89036);