Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×D9×(C3⋊D3)⋊C3 |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C22 |
| derived | C32×C9 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D9×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C32×C9 | C22×C32 |
| Frattini | C32 | C32×D32 |
| Fitting | C3×C9×H(3,𝔽3) | C22 |
| socle | C33 | C3×D32 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
700 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C3⋊D3)⋊C3×AGL(1,ℤ/9), #72254049, D9×#92262, … |
| maximal normal subgroup of | C3×(C3⋊D3)⋊C3×AGL(1,ℤ/9), #72254049, D9×#92262, … |
| maximal quotient of | D9×#92262 |
Past the SmallGroups library coverage — no SmallGroups id.