Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3 |
| derived, Sylow | C31 ⋊ C2×C32×C25 |
| Hall | C3×(C31⋊C3)⋊C25 ⋊ C2 |
| Hall | D31⋊C25 ⋊ C32 |
| Hall | C31⋊C25 ⋊ C2×C32 |
| Hall | C3×D31⋊C3 ⋊ C25 |
| Hall | C3×C31⋊C3 ⋊ C2×C25 |
| Hall | D31 ⋊ C32×C25 |
72 conjugacy classes of subgroups.
465 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, 20);