Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #13486 |
296 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=e,c^2=d,d^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,f^a=fh,i^a=i^6,c^b=cf,d^b=dh,e^b=eh,f^b=fg,g^b=gh,f^c=fgh,g^c=gh130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 89391);