Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×C3⋊AGL(1,𝔽7) |
| unambiguous semidirect product | C3⋊(C9×AGL(1,𝔽7)) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D3×C9) |
| Fitting | C3×C7×C9 ⋊ C2×C3 |
| derived | C3×C7 ⋊ C2×C3×C9 |
| Hall | C3×C9×ΓL(1,𝔽8) ⋊ C2 |
| Sylow | C7 ⋊ C3×D3×C9 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C9×ΓL(1,𝔽8)⋊D9, #72229940, 3−1+2×C3⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | 3−1+2×C3⋊AGL(1,𝔽7), D3×C9×AGL(1,𝔽7), D9×C3⋊AGL(1,𝔽7), … |
| maximal quotient of | C9×ΓL(1,𝔽8)⋊D9, #72229940 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 163);