Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((D31⋊C3)⋊C25) |
| unambiguous semidirect product | (C3⋊(D31⋊C3))⋊C25 |
| unambiguous semidirect product | ((C31⋊C3)⋊C25)⋊D3 |
| unambiguous semidirect product | (C3⋊(D31⋊C25))⋊C3 |
| derived | C3×C31 ⋊ C2×C3×C25 |
| Hall | C3×(C31⋊C3)⋊C25 ⋊ C2 |
| Hall | C31⋊C25 ⋊ C3×D3 |
| Hall | C3⋊(D31⋊C3) ⋊ C25 |
| Hall | C3×C31⋊C3 ⋊ C2×C25 |
| Sylow | C31 ⋊ C3×D3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C3⋊AGL(1,𝔽31) |
| commutator, hypocenter | C3×C31 | C2×C3×C25 |
| Fitting, socle, cosocle | C3×C5×C31 | C2×C3×C5 |
| prime radical | C5×C3⋊(D31⋊C3) | C5 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C5 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,3,31,5|c^5=f,d^a=d^2,e^a=e^30,e^b=e^5,e^c=e^16240 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(D31⋊C3)⋊C25, C2×C3⋊((D31⋊C3)⋊C25) |
| maximal normal subgroup of | D3×(D31⋊C3)⋊C25, C2×C3⋊((D31⋊C3)⋊C25) |
| maximal quotient of | C3⋊(((C31⋊C3)⋊C4)⋊C25), C2×C3⋊((D31⋊C3)⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 21);