Finite Group DatabasebetaFinite Group Databasebeta| order | 15870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D529 |
| unambiguous semidirect product | C529⋊(C2×C3×C5) |
| Fitting, Hall | C3×C5×C529 ⋊ C2 |
| derived, Sylow | C529 ⋊ C2×C3×C5 |
| Hall | C5×C529 ⋊ C2×C3 |
| Hall | C3×C529 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D529 |
| commutator, cosocle, hypocenter | C529 | C2×C3×C5 |
| Frattini | C23 | C3×C5×D23 |
| Fitting | C3×C5×C529 | C2 |
| socle | C3×C5×C23 | D23 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
3990 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D529, C5×D3×D529, D15×D529, … |
| maximal normal subgroup of | C3×D5×D529, C5×D3×D529, D15×D529, … |
| maximal quotient of | C3×C5×Dic529, C2×C3×C5×D529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15870, 2);