Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#327 ⋊ C2 |
| Sylow | C3 ⋊ #10403 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|c^2=dg,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fh,c^b=cf,e^b=eh,f^b=fg,i^b=i^2,e^c=eg,f^c=fg,i^c=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 72896);