Finite Group DatabasebetaFinite Group Databasebeta| order | 15686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | D31×C23⋊C11 |
| unambiguous semidirect product | C31⋊(C2×C23⋊C11) |
| unambiguous semidirect product | (C23×D31)⋊C11 |
| Fitting, socle, derived, Hall | C23×C31 ⋊ C2×C11 |
| Hall | C31×C23⋊C11 ⋊ C2 |
| Hall | C23×D31 ⋊ C11 |
| Sylow | C31 ⋊ C2×C23⋊C11 |
| Sylow | C23 ⋊ C11×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C31 | C2×C11 |
| LCS | G ▷ C23×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 713 |
221 conjugacy classes — view the full character table.
| maximal subgroup of | D31×AGL(1,𝔽23), C2×D31×C23⋊C11 |
| maximal normal subgroup of | D31×AGL(1,𝔽23), C2×D31×C23⋊C11 |
| maximal quotient of | Dic31×C23⋊C11, C2×D31×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15686, 10);