Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| isoclinism | isoclinic class of D201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D201 |
| unambiguous semidirect product | C3⋊(C25×D67) |
| unambiguous semidirect product | C67⋊(D3×C25) |
| Fitting, Hall | C3×C25×C67 ⋊ C2 |
| derived, Hall | C3×C67 ⋊ C2×C25 |
| Hall | C25×C67 ⋊ D3 |
| Hall | C3×C25 ⋊ D67 |
| Sylow | C67 ⋊ D3×C25 |
| Sylow | C3 ⋊ C25×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D201 |
| commutator, hypocenter | C3×C67 | C2×C25 |
| Frattini | C5 | C5×D201 |
| Fitting | C3×C25×C67 | C2 |
| socle, cosocle | C3×C5×C67 | C2×C5 |
| prime radical | C5×D201 | C5 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
2550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C25×D67, D25×D201, D75⋊D67, … |
| maximal normal subgroup of | D3×C25×D67, D25×D201, D75⋊D67, … |
| maximal quotient of | C25×Dic201, C2×C25×D201, C25×D603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 7);