Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×C4×C4⋊Q8 ⋊ C2 |
| Sylow | C3 ⋊ #34216 |
2422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=h,b^2=gh,c^2=g,d^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^d=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 330031);