Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#1807 ⋊ C2 |
| Sylow | C7 ⋊ #8626 |
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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=f,b^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,e^c=eg,f^c=fgh,i^c=i^6172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 62537);