Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of C22⋊(C31⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C31⋊C9) |
| unambiguous semidirect product | C31⋊(C22⋊C9) |
| derived, Hall | C22×C31 ⋊ C9 |
| Sylow | C31 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C31⋊C3) |
| commutator, hypocenter | C22×C31 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C31 | C3 |
| LCS | G ▷ C22×C31 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
Polycyclic presentation:
3^2,2^2,31|a^3=b,c^a=cd,d^a=c,e^a=e^5132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 11);