Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | D4×C9⋊SL(2,𝔽3) |
| unambiguous semidirect product | C4⋊(C2×C9⋊SL(2,𝔽3)) |
| unambiguous semidirect product | (D4×C9)⋊SL(2,𝔽3) |
| Fitting | D4×Q8×C9 ⋊ C3 |
| Sylow | D4×Q8 ⋊ 3−1+2 |
385 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18189);