Finite Group DatabasebetaFinite Group Databasebeta| order | 10166 |
| automorphism | Aut(G) order 21470592 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5083 |
| unambiguous semidirect product | C13⋊D391 |
| unambiguous semidirect product | C17⋊D299 |
| unambiguous semidirect product | C23⋊D221 |
| Fitting, socle, derived, Hall | C13×C17×C23 ⋊ C2 |
| Hall | C17×C23 ⋊ D13 |
| Hall | C13×C23 ⋊ D17 |
| Hall | C13×C17 ⋊ D23 |
| Sylow | C23 ⋊ D221 |
| Sylow | C17 ⋊ D299 |
| Sylow | C13 ⋊ D391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C17×C23 | C2 |
| LCS | G ▷ C13×C17×C23 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,17,23|b^a=b^12,c^a=c^16,d^a=d^222543 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D221, D17×D299, D13×D391, … |
| maximal normal subgroup of | D23×D221, D17×D299, D13×D391, … |
| maximal quotient of | Dic5083, C2×D5083, C3×D5083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10166, 8);