Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | D4×C9×SL(2,𝔽3) |
| unambiguous semidirect product | C4⋊(C2×C9×SL(2,𝔽3)) |
| Fitting | D4×Q8×C9 ⋊ C3 |
| Sylow | D4×Q8 ⋊ C3×C9 |
455 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 455 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18188);