Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #20569⋊C3 |
| Fitting, Sylow | #20569 ⋊ C3 |
300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
Polycyclic presentation:
3,2^8|b^2=g,c^2=h,d^2=fg,e^2=f,g^2=i,b^a=beh,e^a=bdgh,c^b=cf,e^b=ef,d^c=df152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083832);