Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C7⋊#4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#4183 |
| Fitting, derived, Hall | C7×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | AΣL(1,𝔽27) ⋊ D7 |
| Sylow | C7 ⋊ #4183 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×AΣL(1,𝔽27) | C2 |
| Frattini | C32 | C3⋊D21 |
| socle | C3×C7 | #272 |
| LCS | G ▷ C7×AΣL(1,𝔽27) | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
Polycyclic presentation:
2,3^2,7,3^2|b^a=b^2,c^a=c^2,d^a=d^6,f^a=f^2,c^b=cef,e^c=ef^264 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C7⋊#4183, #72249201, #72249208, … |
| maximal normal subgroup of | C3×C7⋊#4183, #72249201, #72249208, … |
| maximal quotient of | C3×C7⋊#4183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 124);