Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C32 · Schur multiplier (H2) = C2 |
| direct product | C3×C32×#272 |
| Fitting | C3×H(3,𝔽3)×C32 ⋊ C2 |
| derived | H(3,𝔽3) ⋊ C2×C3×C32 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×C32 |
616 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C32×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C3×C32×((C3⋊D3)⋊C3)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.