Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C3 |
| direct product | M16×PSU(3,𝔽2)⋊C3 |
| Fitting | C32×M16 ⋊ SL(2,𝔽3) |
364 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
100 conjugacy classes — view the full character table.
| maximal subgroup of | M16×AGL(2,𝔽3), AGL(1,ℤ/8)×PSU(3,𝔽2)⋊C3, #72220196, … |
| maximal normal subgroup of | M16×AGL(2,𝔽3), AGL(1,ℤ/8)×PSU(3,𝔽2)⋊C3, #72220196, … |
| maximal quotient of | #97×PSU(3,𝔽2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.