Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×A5 |
| unambiguous semidirect product | C3⋊(C2×C5×A5) |
| Fitting | C3×C5 ⋊ C2×A5 |
| socle | C3×C5×A5 ⋊ C2 |
| derived | C3×A5 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×A5 |
| commutator, hypocenter | C3×A5 | C2×C5 |
| Frattini | C1 | G |
| Fitting | C3×C5 | C2×A5 |
| socle | C3×C5×A5 | C2 |
| cosocle | C3 | C2×C5×A5 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C5 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 75 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×A5 |
| maximal normal subgroup of | D3×D5×A5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 560);