Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D7⋊C27) |
| unambiguous semidirect product | D21⋊C27 |
| unambiguous semidirect product | (C7⋊C27)⋊D3 |
| derived | C3×C7 ⋊ C2×C27 |
| Hall | C3×C7⋊C27 ⋊ C2 |
| Sylow | C7 ⋊ D3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C3⋊AGL(1,𝔽7) |
| commutator, hypocenter | C3×C7 | C2×C27 |
| Fitting, cosocle | C3×C7×C9 | C2×C3 |
| socle | C32×C7 | C2×C9 |
| prime radical | C3×D21 | C9 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C9 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
Polycyclic presentation:
2,3^4,7|b^3=c,c^3=d,e^a=e^2,f^a=f^6,f^b=f^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 46);