Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C5×Dic3 |
| unambiguous semidirect product | (C2×C3)⋊(C32×C4×C5) |
| derived | C3 ⋊ C2×C32×C4×C5 |
| Hall | C33×C5 ⋊ C2×C4 |
| Sylow | C33 ⋊ C2×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32×C5 | D3 |
| commutator, hypocenter | C3 | C2×C32×C4×C5 |
| Frattini | C2 | C2×C32×C5×D3 |
| Fitting, socle, prime radical | C22×C33×C5 | C2 |
| cosocle | C2×C3 | C22×C32×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C32×C5 | |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 457);