Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×C3×C9×C22⋊A4 |
| Fitting | C25×C3×C9 ⋊ C3 |
| derived | C24 ⋊ C2×C32×C9 |
| Sylow | C25 ⋊ C32×C9 |
1900 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1900 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72229223, C2×C22⋊A4×C9⋊C9, C2×#72229281, … |
| maximal normal subgroup of | C2×#72229223, C2×C22⋊A4×C9⋊C9, C2×#72229281, … |
| maximal quotient of | C2×C22⋊A4×C9⋊C9 |
Past the SmallGroups library coverage — no SmallGroups id.