Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C16 · Schur multiplier (H2) = C2×C32 |
| direct product | C16×C22⋊H(3,𝔽3) |
| unambiguous semidirect product | (C22×C16)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C32×C16)⋊A4 |
| unambiguous semidirect product | (C3×A4×C16)⋊C3 |
| Fitting | C22×C32×C16 ⋊ C3 |
| Sylow | C22×C16 ⋊ H(3,𝔽3) |
188 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7327);