Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×#92302 |
| Fitting, Sylow | C3×#6891 ⋊ C22 |
| derived | C3×C32⋊C9 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C3⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C3×C32⋊C9 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×#6891 | C22 |
| socle | C33 | C2×C3×C3⋊D3 |
| LCS | G ▷ C3×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
1187 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 1187 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | #72269402, #72277465 |
| maximal quotient of | #72269402 |
Past the SmallGroups library coverage — no SmallGroups id.