Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #67361 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C7×C9 ⋊ C2×C9 |
| Hall | #10588035 ⋊ C2 |
| Sylow | C7 ⋊ D9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #67361 |
| commutator, hypocenter | C7×C9 | C2×C9 |
| Frattini | C32 | D3×ΓL(1,𝔽8) |
| Fitting, cosocle | C3×C7×C9 | C2×C3 |
| socle | C32×C7 | C3×D3 |
| prime radical | C3×C7×D9 | C3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C3 | |
44 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,f^a=f^2,d^b=df,e^b=e^266 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×D9⋊C9, #72229906, #72229912, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×D9⋊C9, #72229906, #72229912, … |
| maximal quotient of | #72249091 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 34);