Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C3×#390 ⋊ C2 |
| Sylow | C3 ⋊ #34258 |
5682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=h,c^2=gh,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^b=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#34258, #72255545, #72270678, … |
| maximal normal subgroup of | D3×#34258, #72255545, #72270678, … |
| maximal quotient of | #72271014, #72271434 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 330610);