Finite Group DatabasebetaFinite Group Databasebeta| order | 13861 |
| automorphism | ? |
| homology | Abelianization (H1) = C83 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C167⋊C83 |
| Fitting, socle, derived, Sylow | C167 ⋊ C83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C167 | C83 |
| LCS | G ▷ C167 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
83,167|b^a=b^2585 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽167), C2×C167⋊C83 |
| maximal normal subgroup of | AGL(1,𝔽167), C2×C167⋊C83 |
| maximal quotient of | C2×C167⋊C83 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13861, 1);