Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #13625 |
290 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 111 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=h,d^2=fgh,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^6,d^b=dfh,e^b=eh,f^b=fg,g^b=gh184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 90044);