Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#1084 |
| derived | H(3,𝔽3) ⋊ C3×C4×C5 |
| Hall | C3×C5×H(3,𝔽3) ⋊ C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C4×C5 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×((C3⋊D3)⋊C3)⋊C4, C3×C4×C5×#272 |
| maximal normal subgroup of | C3×C5×((C3⋊D3)⋊C3)⋊C4, C3×C4×C5×#272 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 243);