Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C32 |
| direct product | C32×C5×#157 |
| Fitting, socle, Hall | C34×C5 ⋊ C4 |
| derived | C32 ⋊ C32×C4×C5 |
| Sylow | C34 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | #157 |
| commutator, hypocenter | C32 | C32×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C4 |
| prime radical | C32×C5×C3⋊D3 | C2 |
| cosocle | C3⋊D3 | C2×C32×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C32×C5 | |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 432);