Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×#92344 |
| Fitting, derived, Sylow | C3×#6908 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×#6908 | C22 |
| Frattini | C32 | D3×C3⋊(C3⋊D3) |
| socle | C32 | C2×C3⋊#272 |
| LCS | G ▷ C3×#6908 | |
| UCS | C1 | |
913 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 913 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #72243786, D3×#13091662, #72243868, … |
| maximal normal subgroup of | D3×#13091662, D3×#92280⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.