Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C169 · Schur multiplier (H2) = C1 |
| direct product | C3×D15×C169 |
| unambiguous semidirect product | C3⋊(C3×D5×C169) |
| unambiguous semidirect product | C5⋊(C3×D3×C169) |
| Fitting, Hall | C32×C5×C169 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C3×C169 |
| Hall | C32×C169 ⋊ D5 |
| Hall | C5×C169 ⋊ C3×D3 |
| Hall | C32×C5 ⋊ C2×C169 |
| Sylow | C32 ⋊ D5×C169 |
| Sylow | C5 ⋊ C3×D3×C169 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5070 |
4563 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D15×D169, C3×D3×D5×C169, C3×D15⋊D169, … |
| maximal normal subgroup of | C3×D15×D169, C3×D3×D5×C169, C3×D15⋊D169, … |
| maximal quotient of | C3×Dic15×C169, C2×C3×D15×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 27);