Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×C4⋊AGL(1,ℤ/9) |
| unambiguous semidirect product | (C2×D36)⋊C32 |
| unambiguous semidirect product | (C2×C3×D36)⋊C3 |
| Fitting | C2×C3×C4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ C2×D4 |
566 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×D4×AGL(1,ℤ/9), C2×C3×C4⋊#4183, C2×D3×C4⋊AGL(1,ℤ/9), … |
| maximal normal subgroup of | C2×C3×D4×AGL(1,ℤ/9), C2×D3×C4⋊AGL(1,ℤ/9), C2×#88646⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2558);