Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#10587382 |
| Fitting, Hall | C3×C5×H(3,𝔽3) ⋊ C4 |
| derived | C5×H(3,𝔽3) ⋊ C3×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ Dic5 |
| Sylow | C5 ⋊ C3×#1088 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 291);