Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#4181 |
| Fitting, derived, Hall | C7×C32⋊C9 ⋊ C2 |
| Sylow | C32⋊C9 ⋊ D7 |
| Sylow | C7 ⋊ #4181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D63 |
| commutator, Fitting, cosocle, hypocenter | C7×C32⋊C9 | C2 |
| Frattini | C32 | C3⋊D21 |
| socle | C32×C7 | C3⋊D3 |
| LCS | G ▷ C7×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
Polycyclic presentation:
2,3^2,7,3^2|c^3=f^2,b^a=b^2,c^a=c^2f,d^a=d^6,f^a=f^2,c^b=ce120 conjugacy classes — view the full character table.
| maximal subgroup of | #72249202, #72254883, #72254885, … |
| maximal normal subgroup of | #72249202, #72254883, #72254885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 122);