Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C169 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D3×C169 |
| unambiguous semidirect product | C3⋊(C22×C5×C169) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C5×C169) |
| Fitting | C2×C3×C5×C169 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C5×C169 |
| Hall | C3×C5×C169 ⋊ C22 |
| Hall | C3×C169 ⋊ C22×C5 |
| Hall | C3×C5 ⋊ C22×C169 |
60 conjugacy classes of subgroups.
5070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D9×C169, C2×C5×D3×C169⋊C3, C5×D32×C169, … |
| maximal normal subgroup of | C2×C5×D3×C169⋊C3, C2×C3×C5×D3×C169 |
| maximal quotient of | C2×C5×D9×C169, C5×D32×C169, C2×C5×C3⋊D3×C169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 49);