Finite Group DatabasebetaFinite Group Databasebeta| order | 15870 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C529 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C529 |
| unambiguous semidirect product | C3⋊(C2×C5×C529) |
| Fitting, Hall | C3×C5×C529 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C529 |
| Hall | C3×C529 ⋊ C2×C5 |
| Hall | C3×C5 ⋊ C2×C529 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
7935 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D529, D3×D5×C529, D3×D2645, … |
| maximal normal subgroup of | C5×D3×D529, D3×D5×C529, D3×D2645, … |
| maximal quotient of | C5×Dic3×C529, C2×C5×D3×C529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15870, 5);