Finite Group DatabasebetaFinite Group Databasebeta| order | 9690 |
| automorphism | Aut(G) order 11162880 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4845 |
| unambiguous semidirect product | C3⋊D1615 |
| unambiguous semidirect product | C5⋊D969 |
| unambiguous semidirect product | C17⋊D285 |
| unambiguous semidirect product | C19⋊D255 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C17×C19 | C2 |
| LCS | G ▷ C3×C5×C17×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,17,19|b^a=b^2,c^a=c^4,d^a=d^16,e^a=e^182424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D255, D17×D285, D15×D323, … |
| maximal normal subgroup of | D19×D255, D17×D285, D15×D323, … |
| maximal quotient of | Dic4845, C2×D4845, D14535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9690, 17);