Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×C4×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #60170 |
2742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=g,d^2=h,f^2=h,b^a=bf,e^a=eh,f^a=fh,f^b=fh,d^c=dh,i^d=i^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033769);