Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D5⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D5⋊#157 |
| unambiguous semidirect product | D5⋊(C3×#157) |
| unambiguous semidirect product | #4380⋊(C2×C3) |
| Fitting, socle, Hall | C33×C5 ⋊ C2×C4 |
| derived | C32×C5 ⋊ C2×C3×C4 |
| Sylow | C33 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C3×#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5⋊#157 |
| commutator, hypocenter | C32×C5 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C33×C5 | C2×C4 |
| prime radical | C3×D5×C3⋊D3 | C2 |
| cosocle | C3⋊D15 | C22×C3 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 510);