Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #8769 |
378 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 378 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=h,c^2=dh,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,e^c=eh,f^c=fg,i^c=i^6139 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 63156);