Finite Group DatabasebetaFinite Group Databasebeta| order | 2268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×3−1+2⋊D7 |
| Fitting, Hall | C3×C7×3−1+2 ⋊ C22 |
| derived | C3×C7×C9 ⋊ C22×C3 |
| Sylow | C3×3−1+2 ⋊ C2×D7 |
| Sylow | C7 ⋊ D3×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C7×C9 | C22×C3 |
| Frattini | C3 | C3×D3×D21 |
| Fitting | C3×C7×3−1+2 | C22 |
| socle | C32×C7 | C2×C3×D3 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 | |
160 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 160 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.
| transitive degree | μt(G) = 126 |
129 conjugacy classes — view the full character table.
| maximal subgroup of | #72230126, D3×ΓL(1,𝔽8)⋊AGL(1,ℤ/9), D3×D7×AGL(1,ℤ/9) |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)⋊AGL(1,ℤ/9), D3×D7×AGL(1,ℤ/9) |
| maximal quotient of | #72230126 |
Past the SmallGroups library coverage — no SmallGroups id.