Finite Group DatabasebetaFinite Group Databasebeta| order | 16290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#13108658⋊C2) |
| unambiguous semidirect product | #13108658⋊D5 |
| Fitting, socle, derived, Hall | C5×C181 ⋊ C2×C9 |
| Hall | C5×#13108658 ⋊ C2 |
| Hall | D905 ⋊ C9 |
| Hall | #13108658 ⋊ D5 |
| Sylow | C181 ⋊ C9×D5 |
| Sylow | C5 ⋊ #13108658⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C181 | C2×C9 |
| prime radical | C5⋊(D181⋊C3) | C3 |
| cosocle | C5×C181⋊C3 | C2×C3 |
| LCS | G ▷ C5×C181 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,181|b^3=c,d^a=d^4,e^a=e^180,e^b=e^39,e^c=e^13286 conjugacy classes — view the full character table.
| maximal subgroup of | #45656446, #45656447, D5×#13108658⋊C2, … |
| maximal normal subgroup of | #45656446, #45656447, D5×#13108658⋊C2, … |
| maximal quotient of | #45656407, C2×C5⋊(#13108658⋊C2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16290, 26);