Finite Group DatabasebetaFinite Group Databasebeta| order | 9350 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C25 · Schur multiplier (H2) = C1 |
| direct product | C11×C25×D17 |
| unambiguous semidirect product | C17⋊(C2×C11×C25) |
| Fitting, Hall | C11×C17×C25 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C11×C25 |
| Hall | C17×C25 ⋊ C2×C11 |
| Hall | C11×C17 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C25 | D17 |
| commutator, hypocenter | C17 | C2×C11×C25 |
| Frattini | C5 | C5×C11×D17 |
| Fitting | C11×C17×C25 | C2 |
| socle | C5×C11×C17 | C2×C5 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C11×C25 | |
24 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C25×#595, C25×C11⋊#595, D11×C25×D17, … |
| maximal normal subgroup of | C11×C25×#595, C25×C11⋊#595, D11×C25×D17, … |
| maximal quotient of | C11×C25×Dic17, C2×C11×C25×D17, C3×C11×C25×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9350, 6);