Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#1312 ⋊ C2 |
| Sylow | C7 ⋊ #12064 |
236 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 236 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) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,c^2=ef,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=cfh,d^a=df,i^a=i^6,c^b=ch,d^b=df,i^b=i^6304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 81437);