Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C23×C32 |
| direct product | 3−1+2×#997 |
| Fitting | 3−1+2×H(5,𝔽2) ⋊ C3 |
| Sylow | H(5,𝔽2) ⋊ C3×3−1+2 |
610 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
121 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×#997, 3−1+2×#5935, #72220106, … |
| maximal normal subgroup of | AGL(1,ℤ/9)×#997, 3−1+2×#5935, #72220106, … |
| maximal quotient of | C2×3−1+2×#997, C9⋊C9×#997 |
Past the SmallGroups library coverage — no SmallGroups id.