Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #8822 |
354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=d,c^2=e,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^b=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#8822, #72226182 |
| maximal normal subgroup of | D3×#8822, #72226182 |
| maximal quotient of | #72226182 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 63368);