Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C33 |
| direct product | C3×C3⋊(C3⋊Dic9) |
| unambiguous semidirect product | C3⋊(C3×C3⋊Dic9) |
| derived | C32×C9 ⋊ C3×C4 |
| Sylow | C33×C9 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊(C3⋊D9) |
| commutator, hypocenter | C32×C9 | C3×C4 |
| Frattini | C2×C3 | C3×C3⋊(C3⋊D3) |
| Fitting | C2×C33×C9 | C2 |
| socle, prime radical | C2×C34 | D3 |
| cosocle | C2×C32×C9 | C2×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2×C3 | |
596 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10619867, C3×#10619868, C3×D9×C3⋊Dic3, … |
| maximal normal subgroup of | C3×#10619867, C3×#10619868, C3×D9×C3⋊Dic3, … |
| maximal quotient of | C3×C3⋊(C3⋊(C9⋊C8)), C2×C3×C3⋊(C3⋊Dic9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 741);