Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#11758084 |
| Fitting, Sylow | C33×H(3,𝔽3) ⋊ C22 |
| derived | C32×H(3,𝔽3) ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11758084 |
| commutator, cosocle, hypocenter | C32×H(3,𝔽3) | C22×C3 |
| Frattini | C3 | C3×C3⋊D32 |
| Fitting | C33×H(3,𝔽3) | C22 |
| socle | C34 | D32 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
2822 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 2822 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C3×#72214385, C3×D3×((C3⋊D3)⋊C3)⋊D3, #72253822, … |
| maximal normal subgroup of | C3×D3×((C3⋊D3)⋊C3)⋊D3, C3×#72224543, C3×#14519184 |
| maximal quotient of | C3×#72214331, #72243991, #72243995, … |
Past the SmallGroups library coverage — no SmallGroups id.