Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C4×C9×D15 |
| Fitting | C3×C4×C5×C9 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C4×C9 |
| Hall | C3×C5×C9 ⋊ C2×C4 |
| Sylow | C3×C9 ⋊ C4×D5 |
| Sylow | C5 ⋊ C4×D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C9 | D15 |
| commutator, hypocenter | C3×C5 | C2×C4×C9 |
| Frattini | C2×C3 | C2×C3×D15 |
| Fitting | C3×C4×C5×C9 | C2 |
| socle, cosocle | C2×C32×C5 | C22×C3 |
| prime radical | C2×C3×D15 | C2×C3 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C4×C9 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 207);