Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#2151 ⋊ C2 |
| Sylow | C7 ⋊ #13447 |
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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|c^2=d,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fg,g^a=gh,i^a=i^6,c^b=cf,d^b=dg,e^b=eg,f^b=fgh,g^b=gh,i^b=i^6208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 89158);