Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of (C3⋊D3)⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C3⋊D3)⋊(C7⋊C9) |
| derived | C32×C7 ⋊ C2×C9 |
| Hall | C32⋊(C7⋊C9) ⋊ C2 |
| Sylow | C7 ⋊ (C3⋊D3)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C3⋊D3)⋊ΓL(1,𝔽8) |
| commutator, hypocenter | C32×C7 | C2×C9 |
| Frattini | C32 | D3×ΓL(1,𝔽8) |
| Fitting, cosocle | C33×C7 | C2×C3 |
| socle | C32×C7 | C3×D3 |
| prime radical | C3×C7×C3⋊D3 | C3 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
Polycyclic presentation:
2,3^4,7|b^3=c,d^a=d^2,e^a=e^2,d^b=de,f^b=f^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 41);