Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #13130 |
390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=df,c^2=d,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,e^c=eg,g^c=gh,i^c=i^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 87362);