Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2535 |
| unambiguous semidirect product | C3⋊(C3×D845) |
| unambiguous semidirect product | C5⋊(C3×D507) |
| Fitting, Hall | C32×C5×C169 ⋊ C2 |
| derived | C3×C5×C169 ⋊ C2×C3 |
| Hall | C32×C169 ⋊ D5 |
| Hall | C5×C169 ⋊ C3×D3 |
| Sylow | C169 ⋊ C3×D15 |
| Hall | C32×C5 ⋊ D169 |
| Sylow | C32 ⋊ D845 |
| Sylow | C5 ⋊ C3×D507 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2535 |
| commutator, cosocle, hypocenter | C3×C5×C169 | C2×C3 |
| Frattini | C13 | C3×D195 |
| Fitting | C32×C5×C169 | C2 |
| socle | C32×C5×C13 | D13 |
| LCS | G ▷ C3×C5×C169 | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5070 |
3807 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D15×D169, C3×D5×D507, C3×D3×D845, … |
| maximal normal subgroup of | C3×D15×D169, C3×D5×D507, C3×D3×D845, … |
| maximal quotient of | C3×Dic2535, C2×C3×D2535 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 28);