Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C3⋊D3×C3⋊AGL(1,ℤ/9) |
| Fitting, Sylow | C33×3−1+2 ⋊ C22 |
| derived | C33×C9 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×C9 | C22×C3 |
| Frattini | C3 | C3×C3⋊D32 |
| Fitting | C33×3−1+2 | C22 |
| socle | C34 | C2×C3×D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
2176 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 2176 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72221985, #72221994, C3⋊D3×#92314, … |
| maximal normal subgroup of | #72243969, (C3⋊D3)⋊C3×C3⋊AGL(1,ℤ/9), #72243994, … |
| maximal quotient of | C3⋊D3×#92314, #72253822, #72253826, … |
Past the SmallGroups library coverage — no SmallGroups id.