Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#2308 ⋊ C2 |
| Sylow | C3 ⋊ #10991 |
3122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^2,c^b=cf,e^b=eh,g^b=gh,i^c=i^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10991, #72245112, #72245417, … |
| maximal normal subgroup of | D3×#10991, #72245112, #72245417, … |
| maximal quotient of | #72248093, #72248712, #72270010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76180);