Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊(C3⋊AGL(1,ℤ/9)) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3⋊(C3⋊AGL(1,ℤ/9)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊AGL(1,ℤ/9)) |
| Fitting | C2×C32×3−1+2 ⋊ C2 |
| derived | C32×C9 ⋊ C22×C3 |
| Sylow | C32×3−1+2 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊AGL(1,ℤ/9)) |
| commutator, cosocle, hypocenter | C32×C9 | C22×C3 |
| Frattini | C3 | C2×C3×C3⋊(C3⋊D3) |
| Fitting | C2×C32×3−1+2 | C2 |
| socle | C2×C33 | C3×D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #14518697, #14518698, #14518699, … |
| maximal normal subgroup of | #14518697, #14518698, #14518699, … |
| maximal quotient of | #14518984, C4×C3⋊(C3⋊AGL(1,ℤ/9)), C4⋊(C3⋊(C3⋊AGL(1,ℤ/9))), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 859);