Finite Group DatabasebetaFinite Group Databasebeta| order | 16134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D2689⋊C3 |
| unambiguous semidirect product | (C2689⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C2689 ⋊ C2×C3 |
| Hall | C2689⋊C3 ⋊ C2 |
| Hall | D2689 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2689 | C2×C3 |
| LCS | G ▷ C2689 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2689 |
Polycyclic presentation:
2,3,2689|c^a=c^2688,c^b=c^391454 conjugacy classes — view the full character table.
| maximal subgroup of | #24924442⋊C3, C2×D2689⋊C3 |
| maximal normal subgroup of | #24924442⋊C3, C2×D2689⋊C3 |
| maximal quotient of | Dic2689⋊C3, C2×D2689⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16134, 1);