Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#2239 ⋊ C2 |
| Sylow | C3 ⋊ #33659 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=eg,d^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^2,d^b=dh,f^b=fh,e^c=eh,f^c=fgh,g^c=gh,i^d=i^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33659, #72270555, #72270563 |
| maximal normal subgroup of | D3×#33659, #72270555, #72270563 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 324484);