Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #13809⋊C3 |
| Fitting, Sylow | #13809 ⋊ C3 |
429 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
3,2^8|b^2=h,c^2=i,d^2=f,e^2=h,b^a=bcei,c^a=cei,d^a=dfh,e^a=ci,h^a=i,i^a=fhi,c^b=cf,d^b=dg,e^c=ef60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083593);