Finite Group DatabasebetaFinite Group Databasebeta| order | 16731 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#13095200 |
| derived, Sylow | C132 ⋊ C9×C11 |
| Hall | C11×C132 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #92788 |
| commutator, hypocenter | C132 | C9×C11 |
| Frattini | C3 | C11×#92788 |
| Fitting, socle, prime radical | C3×C11×C132 | C3 |
| cosocle | C3×C132 | C3×C11 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3×C11 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16731 |
1947 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15690148, C11×#15690150, C11⋊#15690148, … |
| maximal normal subgroup of | C11×#15690148, C11×#15690150, C11⋊#15690148, … |
| maximal quotient of | C2×C11×#13095200 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16731, 7);