Finite Group DatabasebetaFinite Group Databasebeta| order | 11350 |
| isoclinism | isoclinic class of D227 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D227 |
| unambiguous semidirect product | C227⋊(C2×C25) |
| Fitting, Hall | C25×C227 ⋊ C2 |
| derived, Sylow | C227 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D227 |
| commutator, hypocenter | C227 | C2×C25 |
| Frattini | C5 | C5×D227 |
| Fitting | C25×C227 | C2 |
| socle, cosocle | C5×C227 | C2×C5 |
| prime radical | C5×D227 | C5 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
2875 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D227, C2×C25×D227, C3×C25×D227, … |
| maximal normal subgroup of | D25×D227, C2×C25×D227, C3×C25×D227 |
| maximal quotient of | C25×Dic227, C2×C25×D227, C3×C25×D227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11350, 3);