Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C92 · Schur multiplier (H2) = C32×C9 |
| direct product | C92×AGL(1,ℤ/9) |
| Fitting, Sylow | C92×3−1+2 ⋊ C2 |
| derived | C9 ⋊ C2×C3×C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C92 | AGL(1,ℤ/9) |
| commutator, hypocenter | C9 | C2×C3×C92 |
| Frattini, socle | C33 | C33×D3 |
| Fitting | C92×3−1+2 | C2 |
| prime radical | C32×AGL(1,ℤ/9) | C32 |
| cosocle | C32×C9 | C2×C33 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C92 | |
1399 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/9)×#6900, AGL(1,ℤ/9)×C9⋊D9, C9×D9×AGL(1,ℤ/9) |
| maximal normal subgroup of | AGL(1,ℤ/9)×#6900, AGL(1,ℤ/9)×C9⋊D9, C9×D9×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.