Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| isoclinism | isoclinic class of D201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D201 |
| unambiguous semidirect product | C3⋊(C52×D67) |
| unambiguous semidirect product | C67⋊(C52×D3) |
| Fitting, socle, Hall | C3×C52×C67 ⋊ C2 |
| derived, Hall | C3×C67 ⋊ C2×C52 |
| Hall | C52×C67 ⋊ D3 |
| Hall | C3×C52 ⋊ D67 |
| Sylow | C67 ⋊ C52×D3 |
| Sylow | C3 ⋊ C52×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D201 |
| commutator, cosocle, hypocenter | C3×C67 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C67 | C2 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
2550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D67, C5×D5×D201, C5×D15⋊D67, … |
| maximal normal subgroup of | C52×D3×D67, C5×D5×D201, C5×D15⋊D67, … |
| maximal quotient of | C52×Dic201, C2×C52×D201, C52×D603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 34);