Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C33 |
| direct product | C3×C5×C3⋊(C3⋊Dic3) |
| unambiguous semidirect product | C3⋊(C3×C5×C3⋊Dic3) |
| derived | C33 ⋊ C3×C4×C5 |
| Hall | C34×C5 ⋊ C4 |
| Sylow | C34 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C3⋊(C3⋊D3) |
| commutator, hypocenter | C33 | C3×C4×C5 |
| Frattini | C2 | C3×C5×C3⋊(C3⋊D3) |
| Fitting, socle, prime radical | C2×C34×C5 | C2 |
| cosocle | C2×C33 | C2×C3×C5 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C3×C5 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 413);