Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C22×C32 |
| direct product | C22×A4×3−1+2 |
| Fitting | C24×3−1+2 ⋊ C3 |
| Sylow | C24 ⋊ C3×3−1+2 |
532 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11758104, A42×3−1+2, C22×#13049240, … |
| maximal normal subgroup of | C22×#11758104, A42×3−1+2, C22×A4×AGL(1,ℤ/9), … |
| maximal quotient of | C22×#11757845, C22×#13049240, C22×A4×#1094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3047);