Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | #67×3−1+2 |
| unambiguous semidirect product | (C9×#67)⋊C3 |
| Fitting | C22×C3×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ D4 |
183 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | #88663⋊C3, #88662⋊C3, #67×AGL(1,ℤ/9), … |
| maximal normal subgroup of | #88663⋊C3, #88662⋊C3, #67×AGL(1,ℤ/9), … |
| maximal quotient of | 3−1+2×Dic3⋊C4, 3−1+2×(C2×D3)⋊C4, 3−1+2×#213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 468);