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 | C3×C3⋊(D7⋊C9) |
| unambiguous semidirect product | C3⋊(C3×D7⋊C9) |
| unambiguous semidirect product | (C3×D21)⋊C9 |
| derived | C3×C7 ⋊ C2×C3×C9 |
| Hall | C32×C7⋊C9 ⋊ C2 |
| Sylow | C7 ⋊ C3×D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊AGL(1,𝔽7) |
| commutator, hypocenter | C3×C7 | C2×C3×C9 |
| Frattini | C3 | C3×C3⋊AGL(1,𝔽7) |
| Fitting, socle | C33×C7 | C2×C3 |
| prime radical | C32×D21 | C3 |
| cosocle | C32×C7 | C2×C32 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C32 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 168);