Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×(#4207⋊C2)⋊C3 |
| Fitting, Sylow | C3×3−1+4 ⋊ C22 |
| derived | #737 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (#4207⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | #737 | C22×C32 |
| Frattini | C3 | C32×#1113 |
| Fitting | C3×3−1+4 | C22 |
| socle | C32 | C3×#1113 |
| LCS | G ▷ #737 | |
| UCS | C1 ◁ C3 | |
1330 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72221983, C3×#72243770, #72243836, … |
| maximal normal subgroup of | D3×(#4207⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.