Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C3 |
| direct product | C31×#157 |
| Fitting, socle, Hall | C32×C31 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #157 |
| commutator, hypocenter | C32 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C31 | C4 |
| prime radical | C3⋊D3×C31 | C2 |
| cosocle | C3⋊D3 | C2×C31 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C31 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 186 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C11×C31×#157, C31×C11⋊#157, C13×C31×#157, … |
| maximal normal subgroup of | C11×C31×#157, C13×C31×#157, C17×C31×#157, … |
| maximal quotient of | C11×C31×#157, C31×C11⋊#157, C13×C31×#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 31);