Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C169⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C5×C169⋊C3) |
| unambiguous semidirect product | (D3×C169)⋊(C3×C5) |
| unambiguous semidirect product | (C5×D3×C169)⋊C3 |
| Fitting | C3×C5×C169 ⋊ C2×C3 |
| derived | C3×C169 ⋊ C2×C3×C5 |
| Hall | C3×C5×C169⋊C3 ⋊ C2 |
| Hall | C3×C169⋊C3 ⋊ C2×C5 |
| Hall | C5×C169 ⋊ C3×D3 |
| Sylow | C169 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×C169⋊C3 |
| commutator, cosocle, hypocenter | C3×C169 | C2×C3×C5 |
| Frattini | C13 | C5×D3×C13⋊C3 |
| Fitting | C3×C5×C169 | C2×C3 |
| socle | C3×C5×C13 | C2×C13⋊C3 |
| LCS | G ▷ C3×C169 | |
| UCS | C1 ◁ C5 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2535 |
885 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D169⋊C3, D3×C5⋊(D169⋊C3), D3×D5×C169⋊C3, … |
| maximal normal subgroup of | C5×D3×D169⋊C3, D3×C5⋊(D169⋊C3), D3×D5×C169⋊C3, … |
| maximal quotient of | C5×Dic3×C169⋊C3, C2×C5×D3×C169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 17);