Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3 |
| direct product | C32×D31⋊C25 |
| unambiguous semidirect product | (C32×D31)⋊C25 |
| derived, Sylow | C31 ⋊ C2×C32×C25 |
| Hall | C32×C31⋊C25 ⋊ C2 |
| Hall | C31⋊C25 ⋊ C2×C32 |
| Hall | C32×D31 ⋊ C25 |
| Hall | C32×C31 ⋊ C2×C25 |
| Hall | D31 ⋊ C32×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D31⋊C5 |
| commutator, hypocenter | C31 | C2×C32×C25 |
| Frattini | C5 | C32×D31⋊C5 |
| Fitting, socle | C32×C5×C31 | C2×C5 |
| prime radical | C32×C5×D31 | C5 |
| cosocle | C5×C31 | C2×C32×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C5 | |
72 conjugacy classes of subgroups.
585 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D31⋊C25, C3⋊D3×D31⋊C25, C2×C32×D31⋊C25 |
| maximal normal subgroup of | C3×D3×D31⋊C25, C3⋊D3×D31⋊C25, C2×C32×D31⋊C25 |
| maximal quotient of | C32×Dic31⋊C25, C2×C32×D31⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 24);