Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#15690146 |
| derived, Hall | C5×#13095201 ⋊ C2 |
| Hall | #13095201 ⋊ D5 |
| Hall | C5×C132 ⋊ D9 |
| Sylow | C132 ⋊ D45 |
| Sylow | C5 ⋊ #15690146 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#13095201 | C2 |
| Frattini | C3 | C5⋊#11759813 |
| Fitting, socle | C3×C5×C132 | D3 |
| LCS | G ▷ C5×#13095201 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
Polycyclic presentation:
2,3,5,13^2,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=e,e^a=d,f^a=f^2,d^b=d^9,e^b=e^3462 conjugacy classes — view the full character table.
| maximal subgroup of | #15690146⋊D5, #44477698, D5×#15690146, … |
| maximal normal subgroup of | #15690146⋊D5, #44477698, D5×#15690146, … |
| maximal quotient of | #44477596, C2×C5⋊#15690146 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 52);