Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#1302 ⋊ C2 |
| Sylow | C7 ⋊ #8917 |
338 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=fh,d^2=g,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^6,d^b=dg,e^b=eh,i^b=i^6,d^c=dh,e^c=egh,i^c=i^6154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 63968);