Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #33326 |
818 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,e^2=g,g^2=h,b^a=bh,i^a=i^2,d^c=dh216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33326 |
| maximal normal subgroup of | D3×#33326 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322218);