Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting | C7×3−1+2 ⋊ C2×C3 |
| derived | C7×C9 ⋊ C2×C32 |
| Hall | ΓL(1,𝔽8)×3−1+2 ⋊ C2 |
| Sylow | C7 ⋊ C3×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C9 | C2×C32 |
| Frattini | C3 | C3×C3⋊AGL(1,𝔽7) |
| Fitting | C7×3−1+2 | C2×C3 |
| socle | C3×C7 | C32×D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
Polycyclic presentation:
2,3^3,7,3|d^3=f^2,d^a=d^2f,e^a=e^6,f^a=f^2,e^b=e^4,d^c=df41 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 167);