Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | D45×C169 |
| unambiguous semidirect product | C5⋊(D9×C169) |
| unambiguous semidirect product | C9⋊(D5×C169) |
| Fitting, Hall | C5×C9×C169 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C2×C169 |
| Hall | C9×C169 ⋊ D5 |
| Hall | C5×C169 ⋊ D9 |
| Sylow | C9 ⋊ D5×C169 |
| Sylow | C5 ⋊ D9×C169 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
4056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D45×D169, D5×D9×C169, D45⋊D169, … |
| maximal normal subgroup of | D45×D169, D5×D9×C169, D45⋊D169, … |
| maximal quotient of | C169×Dic45, C2×D45×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 11);