Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C31⋊C25 |
| unambiguous semidirect product | C3⋊(D3×C31⋊C25) |
| unambiguous semidirect product | (C3⋊D3×C31)⋊C25 |
| derived, Hall | C32×C31 ⋊ C2×C25 |
| Hall | C32×C31⋊C25 ⋊ C2 |
| Hall | C3⋊D3×C31 ⋊ C25 |
| Sylow | C31 ⋊ C3⋊D3×C25 |
| Sylow | C32 ⋊ C2×C31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C3⋊D3×ΓL(1,𝔽32) |
| commutator, hypocenter | C32×C31 | C2×C25 |
| Fitting, socle, cosocle | C32×C5×C31 | C2×C5 |
| prime radical | C5×C3⋊D3×C31 | C5 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×D31⋊C25, (C3⋊D3)⋊(D31⋊C25), D32×C31⋊C25, … |
| maximal normal subgroup of | C3⋊D3×D31⋊C25, (C3⋊D3)⋊(D31⋊C25), D32×C31⋊C25, … |
| maximal quotient of | C3⋊Dic3×C31⋊C25, C2×C3⋊D3×C31⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 28);