Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #12981 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=df,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^2,e^b=eh,i^b=i^2,d^c=dh,f^c=fh120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12981, #72270380, #72270390 |
| maximal normal subgroup of | D3×#12981, #72270380, #72270390 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 86453);