Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#2014 ⋊ C2 |
| Sylow | C3 ⋊ #23430 |
2706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
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,i^a=i^2,c^b=cg,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,f^c=fh,i^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23430 |
| maximal normal subgroup of | D3×#23430 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196723);