Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#3449 ⋊ C2 |
| Sylow | C3 ⋊ #23412 |
1948 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,i^a=i^2,c^b=cg,e^b=eh,e^c=eh,f^c=fh90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23412, #72253881, #72253902 |
| maximal normal subgroup of | D3×#23412, #72253881, #72253902 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196578);