Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting | C3×C25×C31 ⋊ C2×C3 |
| derived, Hall | C25×C31 ⋊ C2×C32 |
| Hall | C3×C25×C31⋊C3 ⋊ C2 |
| Hall | D775 ⋊ C32 |
| Hall | C3×C31⋊C3 ⋊ D25 |
| Sylow | C31 ⋊ C32×D25 |
| Sylow | C25 ⋊ C3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C25⋊(D31⋊C3) |
| commutator, cosocle, hypocenter | C25×C31 | C2×C32 |
| Frattini | C5 | C3×C5⋊(D31⋊C3) |
| Fitting | C3×C25×C31 | C2×C3 |
| socle | C3×C5×C31 | C3×D5 |
| LCS | G ▷ C25×C31 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
501 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D25×D31⋊C3, D3×C25⋊(D31⋊C3), D75⋊(D31⋊C3), … |
| maximal normal subgroup of | C3×D25×D31⋊C3, D3×C25⋊(D31⋊C3), D75⋊(D31⋊C3), … |
| maximal quotient of | C3×(C31⋊C3)⋊Dic25, C2×C3×C25⋊(D31⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 30);