Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | SD16×AΓL(1,𝔽9) |
| Fitting | C32×SD16 ⋊ SD16 |
| Sylow | C32 ⋊ SD162 |
865 conjugacy classes of subgroups.
63 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×AGL(2,𝔽3), AGL(1,ℤ/8)×AΓL(1,𝔽9), GL(2,𝔽3)×AΓL(1,𝔽9), … |
| maximal normal subgroup of | AGL(1,ℤ/8)×AΓL(1,𝔽9) |
| maximal quotient of | AΓL(1,𝔽9)2 |
Past the SmallGroups library coverage — no SmallGroups id.