Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C33 |
| direct product | C33×Dic15 |
| unambiguous semidirect product | C3⋊(C33×Dic5) |
| derived | C3×C5 ⋊ C33×C4 |
| Hall | C34×C5 ⋊ C4 |
| Sylow | C34 ⋊ Dic5 |
| Sylow | C5 ⋊ C33×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C33 | D15 |
| commutator, hypocenter | C3×C5 | C33×C4 |
| Frattini | C2 | C33×D15 |
| Fitting, socle, prime radical | C2×C34×C5 | C2 |
| cosocle | C2×C3×C5 | C2×C33 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C33 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 410);