Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊(C7⋊#272) |
| unambiguous semidirect product | C7⋊(C3⋊#272) |
| Fitting, derived, Hall | C3×C7×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ D7 |
| Sylow | C7 ⋊ C3⋊#272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊(C3⋊D21) |
| commutator, Fitting, cosocle, hypocenter | C3×C7×H(3,𝔽3) | C2 |
| socle | C32×C7 | C3⋊D3 |
| LCS | G ▷ C3×C7×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
Polycyclic presentation:
2,3^3,7,3|b^a=b^2,c^a=c^2,d^a=d^2,e^a=e^6,d^c=df120 conjugacy classes — view the full character table.
| maximal subgroup of | #72249200, #72254861, #72254867, … |
| maximal normal subgroup of | #72249200, #72254861, #72254867, … |
| maximal quotient of | #72249197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 232);