Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C33 |
| direct product | C9×C3⋊(C3⋊Dic3) |
| unambiguous semidirect product | C3⋊(C9×C3⋊Dic3) |
| derived | C33 ⋊ C4×C9 |
| Sylow | C33×C9 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C3⋊(C3⋊D3) |
| commutator, hypocenter | C33 | C4×C9 |
| Frattini | C2×C3 | C3×C3⋊(C3⋊D3) |
| Fitting | C2×C33×C9 | C2 |
| socle, prime radical, cosocle | C2×C34 | C2×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C9 | |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C9×C3⋊Dic3, C9×Dic3×C3⋊D3, C9×#6290, … |
| maximal normal subgroup of | D3×C9×C3⋊Dic3, C9×Dic3×C3⋊D3, C9×#6290, … |
| maximal quotient of | C9×C3⋊(C3⋊(C3⋊C8)), C2×C9×C3⋊(C3⋊Dic3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 742);