Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D31⋊C9)⋊C25 |
| unambiguous semidirect product | (D31⋊C25)⋊C9 |
| unambiguous semidirect product | ((C31⋊C9)⋊C25)⋊C2 |
| derived, Sylow | C31 ⋊ C2×C9×C25 |
| Hall | (C31⋊C9)⋊C25 ⋊ C2 |
| Hall | D31⋊C25 ⋊ C9 |
| Hall | C31⋊C25 ⋊ C2×C9 |
| Hall | D31⋊C9 ⋊ C25 |
| Hall | C31⋊C9 ⋊ C2×C25 |
| Hall | D31 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C5 | AGL(1,𝔽31) |
| commutator, hypocenter | C31 | C2×C9×C25 |
| Fitting, socle, cosocle | C3×C5×C31 | C2×C3×C5 |
| prime radical | C3×C5×D31 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,31,3,5|b^3=e,c^5=f,d^a=d^30,d^b=d^5,d^c=d^16465 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D31⋊C9)⋊C25 |
| maximal normal subgroup of | C2×(D31⋊C9)⋊C25 |
| maximal quotient of | (Dic31⋊C9)⋊C25, C2×(D31⋊C9)⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 2);