Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C139⋊C3 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C139)⋊C3 |
| Fitting, socle, derived, Hall | C5×C139 ⋊ C3×C4 |
| Hall | AGL(1,𝔽5)×C139 ⋊ C3 |
| Hall | C5×C139⋊C3 ⋊ C4 |
| Sylow | C139 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C139 | C3×C4 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
245 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×C139⋊C3, ΓL(1,𝔽16)×C139⋊C3 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×C139⋊C3 |
| maximal quotient of | AGL(1,𝔽5)×C139⋊C9, C3×AGL(1,𝔽5)×C139⋊C3, ΓL(1,𝔽16)×C139⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 15);