Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(D31⋊C25) |
| unambiguous semidirect product | D279⋊C25 |
| unambiguous semidirect product | (C31⋊C25)⋊D9 |
| derived, Hall | C9×C31 ⋊ C2×C25 |
| Hall | C9×C31⋊C25 ⋊ C2 |
| Hall | C31⋊C25 ⋊ D9 |
| Hall | D279 ⋊ C25 |
| Sylow | C31 ⋊ D9×C25 |
| Sylow | C9 ⋊ D31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C9⋊(D31⋊C5) |
| commutator, hypocenter | C9×C31 | C2×C25 |
| Frattini | C3×C5 | C3⋊(D31⋊C5) |
| Fitting, cosocle | C5×C9×C31 | C2×C5 |
| socle | C3×C5×C31 | C5×D3 |
| prime radical | C5×D279 | C5 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,31,3,5|b^5=f,c^3=e^2,c^a=c^2e,d^a=d^30,e^a=e^2,d^b=d^16285 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D31⋊C25, C2×C9⋊(D31⋊C25) |
| maximal normal subgroup of | D9×D31⋊C25, C2×C9⋊(D31⋊C25) |
| maximal quotient of | C9⋊(Dic31⋊C25), C2×C9⋊(D31⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 6);