Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #33333 |
1162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,f^2=g,g^2=h,b^a=be,d^a=dh,c^b=ch,i^b=i^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322245);