Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C3 ⋊ #20370 |
908 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,c^2=e,e^2=h,b^a=be,g^a=gh,f^b=fh,d^c=dh,i^c=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20370, #72271749, #72271756, … |
| maximal normal subgroup of | D3×#20370, #72271749, #72271756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 167074);