Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(D169⋊C3) |
| unambiguous semidirect product | (C2×C5)⋊(D169⋊C3) |
| unambiguous semidirect product | (C2×C169⋊C3)⋊D5 |
| unambiguous semidirect product | (C2×D845)⋊C3 |
| Fitting | C2×C5×C169 ⋊ C2×C3 |
| derived, Hall | C5×C169 ⋊ C22×C3 |
| Hall | C2×D845 ⋊ C3 |
| Hall | C5×C169⋊C3 ⋊ C22 |
| Hall | C169⋊C3 ⋊ C2×D5 |
| Sylow | C169 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(D169⋊C3) |
| commutator, cosocle, hypocenter | C5×C169 | C22×C3 |
| Frattini | C13 | C2×C5⋊(D13⋊C3) |
| Fitting | C2×C5×C169 | C2×C3 |
| socle | C2×C5×C13 | D13⋊C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
304 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C5⋊(D169⋊C3), C2×C3×C5⋊(D169⋊C3), C2×C3⋊(C5⋊(D169⋊C3)) |
| maximal normal subgroup of | C2×C3×C5⋊(D169⋊C3) |
| maximal quotient of | C2×C5⋊(D169⋊C9), D3×C5⋊(D169⋊C3), C2×C3×C5⋊(D169⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 23);