Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×D9⋊C27 |
| unambiguous semidirect product | D9⋊(C2×C27) |
| unambiguous semidirect product | (C2×D9)⋊C27 |
| unambiguous semidirect product | (C9⋊C27)⋊C22 |
| unambiguous semidirect product | (C2×C9⋊C27)⋊C2 |
| Fitting | C2×C9⋊C27 ⋊ C2 |
| derived | C9 ⋊ C22×C27 |
| Sylow | C9⋊C27 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | AGL(1,ℤ/9) |
| commutator, hypocenter | C9 | C22×C27 |
| Frattini | C3×C9 | C2×C3×D3 |
| Fitting | C2×C9⋊C27 | C2 |
| socle | C2×C32 | D3×C9 |
| prime radical | C2×C3×D9 | C9 |
| cosocle | C92 | C22×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C9 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D9⋊C27, C4⋊(D9⋊C27), #611⋊C27, … |
| maximal normal subgroup of | C4×D9⋊C27, C4⋊(D9⋊C27), #611⋊C27, … |
| maximal quotient of | Dic18⋊C27, C4×D9⋊C27, C4⋊(D9⋊C27), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 214);