Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#92264⋊C2 |
| Fitting, Sylow | C3×#6896 ⋊ C22 |
| derived | C92 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92264⋊C2 |
| commutator, cosocle, hypocenter | C92 | C22×C32 |
| Frattini | C32 | C32×D32 |
| Fitting | C3×#6896 | C22 |
| socle | C33 | C3×D32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C3 | |
496 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,ℤ/9)2, #72243341, #72243343, … |
| maximal normal subgroup of | C3×AGL(1,ℤ/9)2, #72243341, #72243343, … |
| maximal quotient of | #72243343, #72243591, #72244044 |
Past the SmallGroups library coverage — no SmallGroups id.