Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C5⋊#15690149 |
| derived, Hall | C5×C132 ⋊ C2×C9 |
| Hall | C5×#13095201 ⋊ C2 |
| Hall | C5⋊(C13⋊D13) ⋊ C9 |
| Hall | #13095201 ⋊ D5 |
| Sylow | C132 ⋊ C9×D5 |
| Sylow | C5 ⋊ #15690149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊#11759816 |
| commutator, hypocenter | C5×C132 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C132 | C2×C3 |
| prime radical | C3×C5⋊(C13⋊D13) | C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
Polycyclic presentation:
2,3,5,13^2,3|b^3=f,c^a=c^4,d^a=d^12,e^a=e^12,d^b=d^3,e^b=e^9456 conjugacy classes — view the full character table.
| maximal subgroup of | #44477637, #44477638, #44477640, … |
| maximal normal subgroup of | #44477637, #44477638, #44477640, … |
| maximal quotient of | #44477589, C2×C5⋊#15690149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 45);