Finite Group DatabasebetaFinite Group Databasebeta| order | 16206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2701 |
| Fitting, socle, Hall | C3×C37×C73 ⋊ C2 |
| derived, Hall | C37×C73 ⋊ C2×C3 |
| Hall | C3×C73 ⋊ D37 |
| Hall | C3×C37 ⋊ D73 |
| Sylow | C73 ⋊ C3×D37 |
| Sylow | C37 ⋊ C3×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2701 |
| commutator, cosocle, hypocenter | C37×C73 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C73 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8103 |
4056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#24925158, C3×#24925159, C3×D37×D73, … |
| maximal normal subgroup of | C3×#24925158, C3×#24925159, C3×D37×D73, … |
| maximal quotient of | C3×Dic2701, C2×C3×D2701 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16206, 8);