Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1379 ⋊ C2 |
| Sylow | C3 ⋊ #12615 |
418 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,d^a=dh,f^a=fh,c^b=ch,i^b=i^2,i^c=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84677);