Finite Group DatabasebetaFinite Group Databasebeta| order | 2268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×ΓL(1,𝔽64) |
| Fitting, derived | C3×C7×C9 ⋊ C22×C3 |
| Hall | C3×#4428 ⋊ C22 |
| Sylow | C7 ⋊ D3×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C9 | C22×C3 |
| Frattini | C3 | D32×ΓL(1,𝔽8) |
| socle | C32×C7 | C2×C3×D3 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 | |
160 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #72230029, D3×ΓL(1,𝔽8)×AGL(1,ℤ/9), D3×#67355⋊C2 |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×AGL(1,ℤ/9), D3×#67355⋊C2 |
| maximal quotient of | #72230029 |
Past the SmallGroups library coverage — no SmallGroups id.