Finite Group DatabasebetaFinite Group Databasebeta| order | 16290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×#13108658 |
| Fitting, socle, Hall | C2×C5×C181 ⋊ C9 |
| derived, Sylow | C181 ⋊ C2×C5×C9 |
| Hall | C5×C181 ⋊ C2×C9 |
| Hall | C2×C181 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #13108658 |
| commutator, hypocenter | C181 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C181 | C9 |
| prime radical | C2×C5×C181⋊C3 | C3 |
| cosocle | C181⋊C3 | C2×C3×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
290 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20266783, #45656407, Dic5×#13108658, … |
| maximal normal subgroup of | C5×#20266783, #45656407, Dic5×#13108658, … |
| maximal quotient of | C4×C5×#13108658, C22×C5×#13108658 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16290, 34);