Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #14910⋊C3 |
| Fitting, Sylow | #14910 ⋊ C3 |
341 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
3,2^8|b^2=h,c^2=f,d^2=g,e^2=h,b^a=bcfhi,c^a=cdi,d^a=cgh,e^a=egh,f^a=fgh,g^a=f,c^b=cf,d^b=dg,e^b=ei,d^c=dh48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083672);