Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic9 |
| unambiguous semidirect product | C9⋊(C4×C31) |
| derived, Sylow | C9 ⋊ C4×C31 |
| Hall | C9×C31 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D9 |
| commutator, hypocenter | C9 | C4×C31 |
| Frattini | C2×C3 | D3×C31 |
| Fitting | C2×C9×C31 | C2 |
| socle, prime radical | C2×C3×C31 | D3 |
| cosocle | C2×C9 | C2×C31 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C31 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1116 |
372 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C31×Dic9, C31×Dic99, C13×C31×Dic9, … |
| maximal normal subgroup of | C11×C31×Dic9, C13×C31×Dic9, C17×C31×Dic9, … |
| maximal quotient of | C11×C31×Dic9, C31×Dic99, C13×C31×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 3);