Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3 |
| direct product | C3×C25×D31⋊C3 |
| unambiguous semidirect product | (C25×D31)⋊C32 |
| unambiguous semidirect product | (C3×C25×D31)⋊C3 |
| Fitting | C3×C25×C31 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C32×C25 |
| Hall | C3×C25×C31⋊C3 ⋊ C2 |
| Hall | C25×D31 ⋊ C32 |
| Hall | C25×C31 ⋊ C2×C32 |
| Hall | C3×C31⋊C3 ⋊ C2×C25 |
| Hall | D31 ⋊ C32×C25 |
72 conjugacy classes of subgroups.
825 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×C25×(C31⋊C3)⋊C4, C2×C3×C25×D31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 29);