Finite Group DatabasebetaFinite Group Databasebeta| order | 11050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D425 |
| unambiguous semidirect product | C17⋊(C13×D25) |
| unambiguous semidirect product | C25⋊(C13×D17) |
| Fitting, Hall | C13×C17×C25 ⋊ C2 |
| derived, Hall | C17×C25 ⋊ C2×C13 |
| Hall | C13×C25 ⋊ D17 |
| Hall | C13×C17 ⋊ D25 |
| Sylow | C25 ⋊ C13×D17 |
| Sylow | C17 ⋊ C13×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D425 |
| commutator, cosocle, hypocenter | C17×C25 | C2×C13 |
| Frattini | C5 | C13×D85 |
| Fitting | C13×C17×C25 | C2 |
| socle | C5×C13×C17 | D5 |
| LCS | G ▷ C17×C25 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
2782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#13133323, C13×#13133324, #36348439, … |
| maximal normal subgroup of | C13×#13133323, C13×#13133324, #36348439, … |
| maximal quotient of | C13×Dic425, C2×C13×D425, C3×C13×D425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11050, 6);