Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×C3⋊Dic15 |
| unambiguous semidirect product | C3⋊(C9×Dic15) |
| derived | C32×C5 ⋊ C4×C9 |
| Hall | C32×C5×C9 ⋊ C4 |
| Sylow | C32×C9 ⋊ Dic5 |
| Sylow | C5 ⋊ C9×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C4×C9 |
| Frattini | C2×C3 | C3×C3⋊D15 |
| Fitting | C2×C32×C5×C9 | C2 |
| socle, prime radical, cosocle | C2×C33×C5 | C2×C3 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C9 | |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 248);