Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×#4175⋊C3 |
| Fitting, Sylow | C3×#6909 ⋊ C22 |
| derived | C34 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C34 | C22×C32 |
| Frattini | C32 | C32×D32 |
| Fitting | C3×#6909 | C22 |
| socle | C32 | C2×C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
601 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 601 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#13091644, #72243942, #72243949, … |
| maximal normal subgroup of | D3×(#4174⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.