Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×D3×C3⋊Dic3 |
| unambiguous semidirect product | (C3×D3)⋊(C5×Dic3) |
| derived, Sylow | C33 ⋊ C2×C4×C5 |
| Hall | C33×C5 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×C3⋊D3 |
| commutator, hypocenter | C33 | C2×C4×C5 |
| Frattini | C2 | C5×D3×C3⋊D3 |
| Fitting, socle | C2×C33×C5 | C22 |
| prime radical | C2×C32×C5×D3 | C2 |
| cosocle | C2×C33 | C22×C5 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C5 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 413);