Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×#63121 |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C3×C4 |
| Hall | C13×#63121 ⋊ C3 |
| Hall | C5×C13×C13⋊C3 ⋊ C4 |
| Hall | C13×C13⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C13⋊C3×#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C3×C4 |
| prime radical | C13⋊C3×D65 | C2 |
| cosocle | C13×D65 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
140 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×#63121⋊C3, C3×C13⋊C3×#63121, C13⋊C3×C3⋊#63121 |
| maximal normal subgroup of | C13⋊C3×#63121⋊C3, C3×C13⋊C3×#63121 |
| maximal quotient of | C13⋊C9×#63121, C3×C13⋊C3×#63121, C13⋊C3×C3⋊#63121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 139);