Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×D27⋊C3 |
| Fitting, Sylow | C9×C27⋊C3 ⋊ C2 |
| derived | C27 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D27⋊C3 |
| commutator, hypocenter | C27 | C2×C3×C9 |
| Frattini | C3×C9 | C32×D3 |
| Fitting | C9×C27⋊C3 | C2 |
| socle | C32 | C32×D9 |
| prime radical | C3×D27⋊C3 | C3 |
| cosocle | C3×C27 | C2×C32 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C9 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C9×AGL(1,ℤ/27), C2×C9×D27⋊C3, #72214313, … |
| maximal normal subgroup of | C9×AGL(1,ℤ/27), C2×C9×D27⋊C3, #72214313, … |
| maximal quotient of | C2×C9×D27⋊C3, #72214313 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 938);