Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1757 ⋊ C2 |
| Sylow | C3 ⋊ #12624 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=e,e^2=h,b^a=bd,c^a=ch,f^a=fg,i^a=i^2,d^b=dg,g^b=gh,f^d=fh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84727);