Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ C22⋊#338 |
1294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,g^a=gh,f^b=fh,i^b=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C22⋊#338, #72269900, #72269904, … |
| maximal normal subgroup of | D3×C22⋊#338, #72269900, #72269904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 74806);