Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C169⋊C3 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C169)⋊C3 |
| Fitting, derived, Hall | C5×C169 ⋊ C3×C4 |
| Hall | AGL(1,𝔽5)×C169 ⋊ C3 |
| Hall | C5×C169⋊C3 ⋊ C4 |
| Sylow | C169 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C169 | C3×C4 |
| Frattini | C13 | AGL(1,𝔽5)×C13⋊C3 |
| socle | C5×C13 | C4×C13⋊C3 |
| prime radical | D5×C169⋊C3 | C2 |
| cosocle | D5×C169 | C2×C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
295 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×C169⋊C3, ΓL(1,𝔽16)×C169⋊C3 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×C169⋊C3 |
| maximal quotient of | AGL(1,𝔽5)×C169⋊C9, C3×AGL(1,𝔽5)×C169⋊C3, ΓL(1,𝔽16)×C169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 15);