Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D31⋊C9) |
| unambiguous semidirect product | (C31⋊C9)⋊D25 |
| unambiguous semidirect product | D775⋊C9 |
| derived, Hall | C25×C31 ⋊ C2×C9 |
| Hall | C25×C31⋊C9 ⋊ C2 |
| Hall | D775 ⋊ C9 |
| Hall | C31⋊C9 ⋊ D25 |
| Sylow | C31 ⋊ C9×D25 |
| Sylow | C25 ⋊ D31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C25⋊(D31⋊C3) |
| commutator, hypocenter | C25×C31 | C2×C9 |
| Frattini | C3×C5 | C5⋊(D31⋊C3) |
| Fitting, cosocle | C3×C25×C31 | C2×C3 |
| socle | C3×C5×C31 | C3×D5 |
| prime radical | C3×D775 | C3 |
| LCS | G ▷ C25×C31 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,31,3,5|b^3=e,c^5=f^4,c^a=c^4f,d^a=d^30,f^a=f^4,d^b=d^25501 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D31⋊C9, C2×C25⋊(D31⋊C9) |
| maximal normal subgroup of | D25×D31⋊C9, C2×C25⋊(D31⋊C9) |
| maximal quotient of | (C31⋊C9)⋊Dic25, C2×C25⋊(D31⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 9);