Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×Q8⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ #11613 |
378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,c^2=f,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,d^b=df,i^b=i^2,i^c=i^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 79399);