Finite Group DatabasebetaFinite Group Databasebeta| order | 16290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊(D181⋊C3) |
| unambiguous semidirect product | C3⋊(C5×D181⋊C3) |
| unambiguous semidirect product | (C5×D543)⋊C3 |
| Fitting, socle | C3×C5×C181 ⋊ C2×C3 |
| derived | C3×C181 ⋊ C2×C3×C5 |
| Hall | C3×C5×C181⋊C3 ⋊ C2 |
| Hall | C3×C181⋊C3 ⋊ C2×C5 |
| Hall | C5×C181 ⋊ C3×D3 |
| Sylow | C181 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(D181⋊C3) |
| commutator, cosocle, hypocenter | C3×C181 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C181 | C2×C3 |
| LCS | G ▷ C3×C181 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
495 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×D181⋊C3, D5×C3⋊(D181⋊C3), D15⋊(D181⋊C3), … |
| maximal normal subgroup of | C5×D3×D181⋊C3, D5×C3⋊(D181⋊C3), D15⋊(D181⋊C3), … |
| maximal quotient of | C5×C3⋊(Dic181⋊C3), C2×C5×C3⋊(D181⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16290, 38);