Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic9⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C2×Dic9)⋊SL(2,𝔽3) |
| derived | Q8×C9 ⋊ C2×C3×C4 |
345 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13230);