Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D169 |
| unambiguous semidirect product | D507⋊D5 |
| unambiguous semidirect product | D845⋊D3 |
| Fitting, derived, Hall | C3×C5×C169 ⋊ C22 |
| Hall | C5×C169 ⋊ C2×D3 |
| Hall | C3×C169 ⋊ C2×D5 |
| Sylow | C169 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D169 |
| Sylow | C5 ⋊ D3×D169 |
| Sylow | C3 ⋊ D5×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C169 | C22 |
| Frattini | C13 | D15⋊D13 |
| socle | C3×C5×C13 | C2×D13 |
| LCS | G ▷ C3×C5×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,13^2|e^13=f^12,c^a=c^2,e^a=e^12f,f^a=f^12,c^b=c^2,d^b=d^4768 conjugacy classes — view the full character table.
| maximal subgroup of | D45⋊D169, D15⋊(D169⋊C3), C3×D15⋊D169, … |
| maximal normal subgroup of | D15⋊(D169⋊C3), C3×D15⋊D169 |
| maximal quotient of | D45⋊D169, C3×D15⋊D169, D845⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 42);