Finite Group DatabasebetaFinite Group Databasebeta| order | 15686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D341 |
| unambiguous semidirect product | C11⋊(C23×D31) |
| unambiguous semidirect product | C31⋊(D11×C23) |
| Fitting, socle, Hall | C11×C23×C31 ⋊ C2 |
| derived, Hall | C11×C31 ⋊ C2×C23 |
| Hall | C23×C31 ⋊ D11 |
| Hall | C11×C23 ⋊ D31 |
| Sylow | C31 ⋊ D11×C23 |
| Sylow | C11 ⋊ C23×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D341 |
| commutator, cosocle, hypocenter | C11×C31 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C31 | C2 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7843 |
3956 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C23×D31, D23×D341, D253⋊D31, … |
| maximal normal subgroup of | D11×C23×D31, D23×D341, D253⋊D31, … |
| maximal quotient of | C23×Dic341, C2×C23×D341 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15686, 7);