Finite Group DatabasebetaFinite Group Databasebeta| order | 16290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C2×C32×C181⋊C5 |
| unambiguous semidirect product | (C2×C32×C181)⋊C5 |
| Fitting, socle, Hall | C2×C32×C181 ⋊ C5 |
| derived, Sylow | C181 ⋊ C2×C32×C5 |
| Hall | C32×C181 ⋊ C2×C5 |
| Hall | C2×C181 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C181⋊C5 |
| commutator, cosocle, hypocenter | C181 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C181 | C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
738 conjugacy classes — view the full character table.
| maximal subgroup of | C32×Dic181⋊C5, C3×C3⋊(Dic181⋊C5), C3×Dic3×C181⋊C5, … |
| maximal normal subgroup of | C32×Dic181⋊C5, C3×C3⋊(Dic181⋊C5), C3×Dic3×C181⋊C5, … |
| maximal quotient of | C32×C4×C181⋊C5, C22×C32×C181⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16290, 42);