Finite Group DatabasebetaFinite Group Databasebeta| order | 17166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2861 |
| unambiguous semidirect product | C2861⋊(C2×C3) |
| Fitting, socle, Hall | C3×C2861 ⋊ C2 |
| derived, Sylow | C2861 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2861 |
| commutator, cosocle, hypocenter | C2861 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2861 | C2 |
| LCS | G ▷ C2861 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8583 |
4296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#26037844, C3⋊#26037844, D3×D2861, … |
| maximal normal subgroup of | C3×#26037844, C3⋊#26037844, D3×D2861, … |
| maximal quotient of | C3×Dic2861, C2×C3×D2861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17166, 2);