Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D507 |
| unambiguous semidirect product | C3⋊(C5×D507) |
| unambiguous semidirect product | C169⋊(C5×C3⋊D3) |
| Fitting, Hall | C32×C5×C169 ⋊ C2 |
| derived, Hall | C32×C169 ⋊ C2×C5 |
| Hall | C5×C169 ⋊ C3⋊D3 |
| Sylow | C169 ⋊ C5×C3⋊D3 |
| Hall | C32×C5 ⋊ D169 |
| Sylow | C32 ⋊ C5×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D507 |
| commutator, cosocle, hypocenter | C32×C169 | C2×C5 |
| Frattini | C13 | C5×C3⋊D39 |
| Fitting | C32×C5×C169 | C2 |
| socle | C32×C5×C13 | D13 |
| LCS | G ▷ C32×C169 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C3⋊D3×D169, D5×C3⋊D507, D845⋊(C3⋊D3), … |
| maximal normal subgroup of | C5×C3⋊D3×D169, D5×C3⋊D507, D845⋊(C3⋊D3), … |
| maximal quotient of | C5×C3⋊Dic507, C2×C5×C3⋊D507 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 30);