Finite Group DatabasebetaFinite Group Databasebeta| order | 9010 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C5×D17×C53 |
| unambiguous semidirect product | C17⋊(C2×C5×C53) |
| Fitting, socle, Hall | C5×C17×C53 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C5×C53 |
| Hall | C17×C53 ⋊ C2×C5 |
| Hall | C5×C17 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C53 | D17 |
| commutator, hypocenter | C17 | C2×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C53 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C5×C53 | |
16 conjugacy classes of subgroups.
2650 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C53×#595, C5×#16813359, C5×D17×D53, … |
| maximal normal subgroup of | C5×C53×#595, C5×#16813359, C5×D17×D53, … |
| maximal quotient of | C5×C53×Dic17, C2×C5×D17×C53, C3×C5×D17×C53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9010, 3);