Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C13 |
| direct product | D5×#13095201 |
| unambiguous semidirect product | C5⋊(C2×#13095201) |
| derived, Hall | C5×C132 ⋊ C2×C9 |
| Hall | C5×#13095201 ⋊ C2 |
| Hall | D5×C132 ⋊ C9 |
| Sylow | C132 ⋊ C9×D5 |
| Sylow | C5 ⋊ C2×#13095201 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×#92789 |
| commutator, hypocenter | C5×C132 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C132 | C2×C3 |
| prime radical | C3×D5×C132 | C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44477656, #44477660, AGL(1,𝔽5)×#13095201, … |
| maximal normal subgroup of | #44477656, #44477660, AGL(1,𝔽5)×#13095201, … |
| maximal quotient of | Dic5×#13095201, C2×D5×#13095201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 50);