Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #9651 |
720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=df,c^2=eg,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,d^b=dg,f^b=fg144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 68401);