Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4×C3⋊D15 |
| Fitting | C33×C4×C5 ⋊ C2 |
| derived | C32×C5 ⋊ C2×C3×C4 |
| Hall | C33×C5 ⋊ C2×C4 |
| Sylow | C33 ⋊ C4×D5 |
| Sylow | C5 ⋊ C3×C4×C3⋊D3 |
240 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, 470);