Finite Group DatabasebetaFinite Group Databasebeta| order | 9486 |
| automorphism | Aut(G) order 13659840 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4743 |
| unambiguous semidirect product | C9⋊D527 |
| unambiguous semidirect product | C17⋊D279 |
| unambiguous semidirect product | C31⋊D153 |
| Fitting, derived, Hall | C9×C17×C31 ⋊ C2 |
| Hall | C17×C31 ⋊ D9 |
| Hall | C9×C31 ⋊ D17 |
| Hall | C9×C17 ⋊ D31 |
| Sylow | C31 ⋊ D153 |
| Sylow | C17 ⋊ D279 |
| Sylow | C9 ⋊ D527 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C17×C31 | C2 |
| Frattini | C3 | D1581 |
| socle | C3×C17×C31 | D3 |
| LCS | G ▷ C9×C17×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,31,3|b^3=e^2,b^a=b^2e,c^a=c^16,d^a=d^30,e^a=e^22373 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D153, D17×D279, D9×D527, … |
| maximal normal subgroup of | D31×D153, D17×D279, D9×D527, … |
| maximal quotient of | Dic4743, C2×D4743, D14229 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9486, 9);