Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D775 |
| unambiguous semidirect product | C25⋊(C32×D31) |
| Fitting, Hall | C32×C25×C31 ⋊ C2 |
| derived, Hall | C25×C31 ⋊ C2×C32 |
| Hall | C32×C31 ⋊ D25 |
| Hall | C32×C25 ⋊ D31 |
| Sylow | C31 ⋊ C32×D25 |
| Sylow | C25 ⋊ C32×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D775 |
| commutator, cosocle, hypocenter | C25×C31 | C2×C32 |
| Frattini | C5 | C32×D155 |
| Fitting | C32×C25×C31 | C2 |
| socle | C32×C5×C31 | D5 |
| LCS | G ▷ C25×C31 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
3501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D25×D31, C3×D3×D775, C3×D75⋊D31, … |
| maximal normal subgroup of | C32×D25×D31, C3×D3×D775, C3×D75⋊D31, … |
| maximal quotient of | C32×Dic775, C2×C32×D775 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 40);