Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C27 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×D3×C27 |
| unambiguous semidirect product | C3⋊(C22×C3×C27) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C3×C27) |
| Fitting | C2×C32×C27 ⋊ C2 |
| derived | C3 ⋊ C22×C3×C27 |
| Sylow | C32×C27 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C27 | D3 |
| commutator, hypocenter | C3 | C22×C3×C27 |
| Frattini | C9 | C2×C32×D3 |
| Fitting | C2×C32×C27 | C2 |
| socle | C2×C33 | C2×C9 |
| prime radical | C2×C32×D3 | C9 |
| cosocle | C3×C9 | C22×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C27 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
486 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×Dic27, C3×#10619544, C3×#10619545, … |
| maximal normal subgroup of | C3×D3×Dic27, C3×#10619544, C3×#10619545, … |
| maximal quotient of | C3×Dic6×C27, C3×C4×D3×C27, C3×D12×C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 613);