Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#3173 ⋊ C2 |
| Sylow | C3 ⋊ #33691 |
524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,d^b=dh,f^b=fh,d^c=dg,e^c=eh,f^c=fg,g^c=gh,i^c=i^2,f^d=fh66 conjugacy classes — view the full character table.
| maximal subgroup of | #72270232, #72270555, D3×#33691 |
| maximal normal subgroup of | #72270232, #72270555, D3×#33691 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 324823);