Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #33638 |
514 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=eg,b^2=e,e^2=h,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fg,g^a=gh,i^a=i^2,d^b=dh,i^b=i^2,f^c=fgh,g^c=gh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72270617, #72270649, D3×#33638, … |
| maximal normal subgroup of | #72270617, #72270649, D3×#33638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 324320);