Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#1291 ⋊ C2 |
| Sylow | C7 ⋊ #9339 |
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 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=dfh,d^2=gh,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^6,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=egh,f^c=fg,i^c=i^6130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 66576);