Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×D9⋊H(3,𝔽3) |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C22 |
664 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D9⋊H(3,𝔽3), #72244036, #72244044, … |
| maximal normal subgroup of | D3×H(3,𝔽3)×AGL(1,ℤ/9), D3×D9⋊((C3⋊D3)⋊C3) |
| maximal quotient of | D9×D9⋊H(3,𝔽3), #72244036, #72244044 |
Past the SmallGroups library coverage — no SmallGroups id.