Finite Group DatabasebetaFinite Group Databasebeta| order | 16290 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C181 · Schur multiplier (H2) = C3 |
| direct product | C32×D5×C181 |
| unambiguous semidirect product | C5⋊(C2×C32×C181) |
| Fitting, socle, Hall | C32×C5×C181 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C32×C181 |
| Hall | C5×C181 ⋊ C2×C32 |
| Hall | C32×C5 ⋊ C2×C181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C181 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C32×C181 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C181 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C32×C181 | |
48 conjugacy classes of subgroups.
6516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×AGL(1,𝔽5)×C181, C32×#16813739, C32×D5×D181, … |
| maximal normal subgroup of | C32×AGL(1,𝔽5)×C181, C32×#16813739, C32×D5×D181, … |
| maximal quotient of | C32×Dic5×C181, C2×C32×D5×C181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16290, 53);