Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | Q8×C3⋊AGL(1,ℤ/9) |
| Fitting | C3×Q8×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ C2×Q8 |
434 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×C3⋊AGL(1,ℤ/9), #41×C3⋊AGL(1,ℤ/9), Q8×#92314 |
| maximal normal subgroup of | SD16×C3⋊AGL(1,ℤ/9), #41×C3⋊AGL(1,ℤ/9) |
| maximal quotient of | C4⋊C4×C3⋊AGL(1,ℤ/9), Q8×#92314 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2649);