Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic31⋊C9 |
| unambiguous semidirect product | (C31⋊C9)⋊C4 |
| derived, Sylow | C31 ⋊ C4×C9 |
| Hall | C31⋊C9 ⋊ C4 |
| Hall | Dic31 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D31⋊C3 |
| commutator, hypocenter | C31 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1116 |
Polycyclic presentation:
2,3,2,3,31|a^2=c,b^3=d,e^a=e^30,e^b=e^566 conjugacy classes — view the full character table.
| maximal subgroup of | C11×Dic31⋊C9, C11⋊(Dic31⋊C9), C13×Dic31⋊C9, … |
| maximal normal subgroup of | C11×Dic31⋊C9, C13×Dic31⋊C9, C17×Dic31⋊C9, … |
| maximal quotient of | C11×Dic31⋊C9, C11⋊(Dic31⋊C9), C13×Dic31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 1);