Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C3×C31×D75 |
| unambiguous semidirect product | C3⋊(C3×C31×D25) |
| unambiguous semidirect product | C25⋊(C3×D3×C31) |
| Fitting, Hall | C32×C25×C31 ⋊ C2 |
| derived | C3×C25 ⋊ C2×C3×C31 |
| Hall | C25×C31 ⋊ C3×D3 |
| Hall | C32×C31 ⋊ D25 |
| Hall | C32×C25 ⋊ C2×C31 |
| Sylow | C25 ⋊ C3×D3×C31 |
| Sylow | C32 ⋊ C31×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C2×C3×C31 |
| Frattini | C5 | C3×D15×C31 |
| Fitting | C32×C25×C31 | C2 |
| socle | C32×C5×C31 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C3×C31 | |
54 conjugacy classes of subgroups.
3627 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D31×D75, C3×D3×C31×D25, C3×D75⋊D31, … |
| maximal normal subgroup of | C3×D31×D75, C3×D3×C31×D25, C3×D75⋊D31, … |
| maximal quotient of | C3×C31×Dic75, C2×C3×C31×D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 43);