Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×D72 |
| Fitting, socle, Hall | C32×C72 ⋊ C23 |
| derived | C3×C72 ⋊ C23×C3 |
| Sylow | C72 ⋊ C22×C3×D3 |
| Sylow | C32 ⋊ C2×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D72 |
| commutator, cosocle, hypocenter | C3×C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72 | C23 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C3 | |
342 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#64423⋊C2, D32×D72, D72×AGL(1,ℤ/9), … |
| maximal normal subgroup of | C3×D3×#64423⋊C2, D32×D72 |
| maximal quotient of | D72×AGL(1,ℤ/9), C3×#72213616, C3×D3×D21⋊D7 |
Past the SmallGroups library coverage — no SmallGroups id.