Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C4×C32 ⋊ C2 |
| Sylow | C3 ⋊ #13549 |
238 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,c^b=ch,i^c=i^2288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 89746);