Finite Group DatabasebetaFinite Group Databasebeta| order | 9590 |
| automorphism | Aut(G) order 15650880 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4795 |
| unambiguous semidirect product | C5⋊D959 |
| unambiguous semidirect product | C7⋊D685 |
| unambiguous semidirect product | C137⋊D35 |
| Fitting, socle, derived, Hall | C5×C7×C137 ⋊ C2 |
| Hall | C7×C137 ⋊ D5 |
| Hall | C5×C137 ⋊ D7 |
| Sylow | C137 ⋊ D35 |
| Hall | C5×C7 ⋊ D137 |
| Sylow | C7 ⋊ D685 |
| Sylow | C5 ⋊ D959 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C137 | C2 |
| LCS | G ▷ C5×C7×C137 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,137|b^a=b^4,c^a=c^6,d^a=d^1362399 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D35×D137, D7×D685, D5×D959, … |
| maximal normal subgroup of | D35×D137, D7×D685, D5×D959, … |
| maximal quotient of | Dic4795, C2×D4795, C3×D4795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9590, 8);