Finite Group DatabasebetaFinite Group Databasebeta| order | 15060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic251⋊C5) |
| unambiguous semidirect product | (C251⋊C5)⋊Dic3 |
| unambiguous semidirect product | Dic753⋊C5 |
| derived, Hall | C3×C251 ⋊ C4×C5 |
| Hall | C3×C251⋊C5 ⋊ C4 |
| Hall | Dic753 ⋊ C5 |
| Hall | C251⋊C5 ⋊ Dic3 |
| Sylow | C251 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ Dic251⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D251⋊C5) |
| commutator, hypocenter | C3×C251 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C251 | C2×C5 |
| prime radical | C2×C3×C251⋊C5 | C2 |
| LCS | G ▷ C3×C251 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3012 |
Polycyclic presentation:
2,3,5,251,2|a^2=e,b^a=b^2,d^a=d^250,d^c=d^219180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15060, 12);