Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C32 |
| direct product | C32×C5×C3⋊Dic3 |
| unambiguous semidirect product | C3⋊(C32×C5×Dic3) |
| derived | C32 ⋊ C32×C4×C5 |
| Hall | C34×C5 ⋊ C4 |
| Sylow | C34 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5 | C3⋊D3 |
| commutator, hypocenter | C32 | C32×C4×C5 |
| Frattini | C2 | C32×C5×C3⋊D3 |
| Fitting, socle, prime radical | C2×C34×C5 | C2 |
| cosocle | C2×C32 | C2×C32×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C32×C5 | |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 411);