Finite Group DatabasebetaFinite Group Databasebeta| order | 16290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C181 ⋊ C2×C3 |
| derived, Hall | C5×C181 ⋊ C2×C32 |
| Hall | C3×C5×C181⋊C3 ⋊ C2 |
| Hall | D905 ⋊ C32 |
| Hall | C3×C181⋊C3 ⋊ D5 |
| Sylow | C181 ⋊ C32×D5 |
| Sylow | C5 ⋊ C3×D181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊(D181⋊C3) |
| commutator, cosocle, hypocenter | C5×C181 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C181 | C2×C3 |
| LCS | G ▷ C5×C181 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
486 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16813737⋊C3, C3×#16813738⋊C3, C3×D5×D181⋊C3, … |
| maximal normal subgroup of | C3×#16813737⋊C3, C3×#16813738⋊C3, C3×D5×D181⋊C3, … |
| maximal quotient of | C3×Dic905⋊C3, C2×C3×C5⋊(D181⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16290, 36);