Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#1387 ⋊ C2 |
| Sylow | C7 ⋊ #13485 |
314 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 87 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=eh,c^2=d,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,i^a=i^6,c^b=cf,f^b=fg,g^b=gh,i^b=i^6,e^c=eh,f^c=fg,g^c=gh136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 89387);