Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #13499 |
276 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 276 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=e,c^2=dg,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,f^a=fh,c^b=cf,f^b=fh,d^c=dh,e^c=eg,f^c=fh,g^c=gh,i^c=i^6208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 89463);