Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| isoclinism | isoclinic class of AGL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×AGL(2,𝔽3) |
| Fitting | C32×C16 ⋊ GL(2,𝔽3) |
| derived | PSU(3,𝔽2)⋊C3 ⋊ C2×C16 |
458 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
176 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C16×AGL(2,𝔽3), C32×AGL(2,𝔽3) |
| maximal normal subgroup of | C3×C16×AGL(2,𝔽3), C32×AGL(2,𝔽3) |
| maximal quotient of | C3×C16×AGL(2,𝔽3), C32×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.