Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34 |
| direct product | C2×C3×#4207⋊C3 |
| Fitting | C2×C3×3−1+4 ⋊ C2 |
| derived | C3×C9 ⋊ C22×C33 |
| Sylow | C3×3−1+4 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4207⋊C3 |
| commutator, cosocle, hypocenter | C3×C9 | C22×C33 |
| Frattini | C3 | C2×C33×C3⋊D3 |
| Fitting | C2×C3×3−1+4 | C2 |
| socle | C2×C32 | C32×C3⋊D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C3 | |
3602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72221867, C2×C3×#13091647, C2×C3×#13091662, … |
| maximal normal subgroup of | C2×#72221867 |
| maximal quotient of | C2×#72221845, AGL(1,𝔽7)×#4207⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.