Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((D31⋊C5)⋊C9) |
| unambiguous semidirect product | (ΓL(1,𝔽32)⋊C9)⋊D5 |
| unambiguous semidirect product | (C5⋊(D31⋊C5))⋊C9 |
| unambiguous semidirect product | (C5⋊(D31⋊C9))⋊C5 |
| derived | C5×C31 ⋊ C2×C5×C9 |
| Hall | C5×ΓL(1,𝔽32)⋊C9 ⋊ C2 |
| Hall | C5⋊(D31⋊C5) ⋊ C9 |
| Hall | C5×ΓL(1,𝔽32) ⋊ C2×C9 |
| Hall | C31⋊C9 ⋊ C5×D5 |
| Sylow | C31 ⋊ C5×C9×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊AGL(1,𝔽31) |
| commutator, hypocenter | C5×C31 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C5×C31 | C2×C3×C5 |
| prime radical | C3×C5⋊(D31⋊C5) | C3 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,31,3|b^3=f,d^a=d^4,e^a=e^30,e^b=e^5,e^c=e^16195 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(D31⋊C5)⋊C9, C2×C5⋊((D31⋊C5)⋊C9) |
| maximal normal subgroup of | D5×(D31⋊C5)⋊C9, C2×C5⋊((D31⋊C5)⋊C9) |
| maximal quotient of | (ΓL(1,𝔽32)⋊C9)⋊Dic5, C2×C5⋊((D31⋊C5)⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 51);