Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×#4184⋊C3 |
| Fitting, Sylow | C3×#6910 ⋊ C22 |
| derived | C3×#731 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#731 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×#6910 | C22 |
| socle | C32 | C2×C3×#272 |
| LCS | G ▷ C3×#731 | |
| UCS | C1 | |
696 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 59 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×#13091662, #72243842, #72243847, … |
| maximal normal subgroup of | D3×(#4176⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.