Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D45 |
| Fitting | C22×C3×C5×C9 ⋊ C2 |
| derived | C5×C9 ⋊ C23×C3 |
| Hall | C3×C5×C9 ⋊ C23 |
| Sylow | C3×C9 ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×C3×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D45 |
| commutator, cosocle, hypocenter | C5×C9 | C23×C3 |
| Frattini | C3 | C22×C3×D15 |
| Fitting | C22×C3×C5×C9 | C2 |
| socle | C22×C32×C5 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C22×C3 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 352);