Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C4×C5×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | C4×C5×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C4×C5 |
| Hall | C5×H(3,𝔽3) ⋊ C22×C4 |
410 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
220 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C5×AGL(2,𝔽3), C3×C4×C5×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C3×C4×C5×((C3⋊D3)⋊C3)⋊C2 |
| maximal quotient of | C3×C4×C5×((C3⋊D3)⋊C3)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.