Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×A4×3−1+2 |
| Fitting | C22×C4×3−1+2 ⋊ C3 |
| Sylow | C22×C4 ⋊ C3×3−1+2 |
284 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 117 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 | C4×#13049240, 3−1+2×#5950, A4×AGL(1,𝔽5)×3−1+2, … |
| maximal normal subgroup of | C4×A4×AGL(1,ℤ/9), C4×S4×3−1+2, C4×A4⋊AGL(1,ℤ/9), … |
| maximal quotient of | C4×#13049240, A4×AGL(1,𝔽5)×3−1+2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2514);