Finite Group DatabasebetaFinite Group Databasebeta| order | 10166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D391 |
| unambiguous semidirect product | C17⋊(C13×D23) |
| unambiguous semidirect product | C23⋊(C13×D17) |
| Fitting, socle, Hall | C13×C17×C23 ⋊ C2 |
| derived, Hall | C17×C23 ⋊ C2×C13 |
| Hall | C13×C23 ⋊ D17 |
| Hall | C13×C17 ⋊ D23 |
| Sylow | C23 ⋊ C13×D17 |
| Sylow | C17 ⋊ C13×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D391 |
| commutator, cosocle, hypocenter | C17×C23 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C23 | C2 |
| LCS | G ▷ C17×C23 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
2561 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D17×D23, D13×D391, D221⋊D23, … |
| maximal normal subgroup of | C13×D17×D23, D13×D391, D221⋊D23, … |
| maximal quotient of | C13×Dic391, C2×C13×D391, C3×C13×D391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10166, 4);