Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊(C5⋊(D31⋊C3))) |
| unambiguous semidirect product | C5⋊(C3⋊(C5⋊(D31⋊C3))) |
| unambiguous semidirect product | (C31⋊C3)⋊(C3⋊(C5⋊D5)) |
| Fitting, socle, derived | C3×C52×C31 ⋊ C2×C3 |
| Hall | C3×C52×C31⋊C3 ⋊ C2 |
| Hall | C52×C31 ⋊ C3×D3 |
| Hall | C3×C31⋊C3 ⋊ C5⋊D5 |
| Sylow | C31 ⋊ C3×C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ C3⋊(D31⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C31 | C2×C3 |
| LCS | G ▷ C3×C52×C31 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5^2,31|c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^30,f^b=f^5492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 132);