Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1279 ⋊ C2 |
| Sylow | C3 ⋊ #8174 |
698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=e,d^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fg,c^b=cgh,i^c=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 60189);