Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D13⋊C9) |
| unambiguous semidirect product | (C13⋊C9)⋊D25 |
| unambiguous semidirect product | D325⋊C9 |
| derived, Hall | C13×C25 ⋊ C2×C9 |
| Hall | C25×C13⋊C9 ⋊ C2 |
| Hall | D325 ⋊ C9 |
| Hall | C13⋊C9 ⋊ D25 |
| Sylow | C25 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ C9×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C25⋊(D13⋊C3) |
| commutator, hypocenter | C13×C25 | C2×C9 |
| Frattini | C3×C5 | C5⋊(D13⋊C3) |
| Fitting | C3×C13×C25 | C2×C3 |
| socle | C3×C5×C13 | C3×D5 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13,3,5|b^3=e,c^5=f^4,c^a=c^4f,d^a=d^12,f^a=f^4,d^b=d^3276 conjugacy classes — view the full character table.
| maximal subgroup of | #13049908⋊C9, #13049907⋊C9, D25×D13⋊C9, … |
| maximal normal subgroup of | #13049908⋊C9, #13049907⋊C9, D25×D13⋊C9, … |
| maximal quotient of | Dic325⋊C9, C2×C25⋊(D13⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 4);