Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#332 ⋊ C2 |
| Sylow | C3 ⋊ #9217 |
610 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,d^2=gh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,f^c=fh,i^c=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 65718);