Finite Group DatabasebetaFinite Group Databasebeta| order | 702 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×C13) |
| unambiguous semidirect product | 3−1+2⋊(C2×C13) |
| Fitting, Hall | C13×3−1+2 ⋊ C2 |
| derived | C9 ⋊ C2×C3×C13 |
| Sylow | 3−1+2 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C9 | C2×C3×C13 |
| Frattini | C3 | C3×D3×C13 |
| Fitting | C13×3−1+2 | C2 |
| socle | C3×C13 | C3×D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C13 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 117 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | D13×AGL(1,ℤ/9), C2×C13×AGL(1,ℤ/9), C13⋊C3×AGL(1,ℤ/9) |
| maximal normal subgroup of | D13×AGL(1,ℤ/9), C2×C13×AGL(1,ℤ/9), C13⋊C3×AGL(1,ℤ/9) |
| maximal quotient of | C13×3−1+2⋊C4, C2×C13×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(702, 35);