Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #33329 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,e^2=g,g^2=h,b^a=bg,f^a=fh,i^a=i^2,e^b=eh,d^c=dh150 conjugacy classes — view the full character table.
| maximal subgroup of | #72222773, D3×#33329, #72258639, … |
| maximal normal subgroup of | D3×#33329, #72258639, #72258667, … |
| maximal quotient of | #72222773 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322230);