Finite Group DatabasebetaFinite Group Databasebeta| order | 15686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D713 |
| unambiguous semidirect product | C31⋊(C11×D23) |
| Fitting, socle, Hall | C11×C23×C31 ⋊ C2 |
| derived, Hall | C23×C31 ⋊ C2×C11 |
| Hall | C11×C31 ⋊ D23 |
| Hall | C11×C23 ⋊ D31 |
| Sylow | C31 ⋊ C11×D23 |
| Sylow | C23 ⋊ C11×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D713 |
| commutator, cosocle, hypocenter | C23×C31 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C31 | C2 |
| LCS | G ▷ C23×C31 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7843 |
3938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D23×D31, D11×D713, D253⋊D31, … |
| maximal normal subgroup of | C11×D23×D31, D11×D713, D253⋊D31, … |
| maximal quotient of | C11×Dic713, C2×C11×D713 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15686, 5);