Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q16×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | Q16×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C22×Q16 |
963 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 963 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
77 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 16063);