Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊D9 |
| derived | C7×C9 ⋊ C2×C9 |
| Hall | C9×C7⋊C9 ⋊ C2 |
| Sylow | C7 ⋊ C9×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ΓL(1,𝔽8)⋊D9 |
| commutator, hypocenter | C7×C9 | C2×C9 |
| Frattini | C32 | C3⋊AGL(1,𝔽7) |
| Fitting, cosocle | C3×C7×C9 | C2×C3 |
| socle | C32×C7 | C3×D3 |
| prime radical | C3×D63 | C3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C3 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
Polycyclic presentation:
2,3^3,7,3|b^3=c,d^3=f,d^a=d^2f^2,e^a=e^6,f^a=f^2,e^b=e^281 conjugacy classes — view the full character table.
| maximal subgroup of | C9×ΓL(1,𝔽8)⋊D9, #72229941, #72229943, … |
| maximal normal subgroup of | C9×ΓL(1,𝔽8)⋊D9, #72229941, #72229943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 47);