Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #60325⋊C3 |
| Fitting, Sylow | #60325 ⋊ C3 |
490 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 490 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) = 192 |
Polycyclic presentation:
3,2^8|b^2=h,f^2=h,h^2=i,b^a=efg,c^a=bcefhi,d^a=cg,e^a=bcdfhi,c^b=cg,d^b=di,e^b=egi,d^c=dgi,f^c=fi,f^d=fi104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084688);