Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D3×D4×SD16 |
| Fitting | C3×D4×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C2×D4×SD16 |
3226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×AGL(1,ℤ/8), D3×#61050, D3×#61071, … |
| maximal normal subgroup of | D3×D4×AGL(1,ℤ/8), D3×#61050, D3×#61071 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1044776);