Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#2110 ⋊ C2 |
| Sylow | C3 ⋊ #12617 |
382 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=e,d^2=h,e^2=g,g^2=h,b^a=bd,i^a=i^2,c^b=cg,d^b=dh,e^b=eh,f^c=fh108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84689);