Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×C4×D9 |
| Fitting | C2×C32×C4×C9 ⋊ C2 |
| derived | C9 ⋊ C22×C32×C4 |
| Sylow | C32×C9 ⋊ C22×C4 |
614 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D9×C3⋊D3, C2×C32×D4×D9, C2×D9×C4⋊(C3⋊D3), … |
| maximal normal subgroup of | C2×C4×D9×C3⋊D3, C2×C32×D4×D9, C2×D9×C4⋊(C3⋊D3), … |
| maximal quotient of | C32×C42×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2541);