Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #60284⋊C3 |
| Fitting, Sylow | #60284 ⋊ C3 |
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
Polycyclic presentation:
3,2^8|b^2=h,f^2=g,h^2=i,c^a=cdfh,d^a=ce,c^b=cg,d^b=di,e^b=egi,f^b=fi,d^c=dgi104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084680);