Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C23 |
| direct product | C22⋊C4×C9⋊A4 |
| unambiguous semidirect product | (C9×C22⋊C4)⋊A4 |
| Fitting | C22×C9×C22⋊C4 ⋊ C3 |
| Sylow | C22×C22⋊C4 ⋊ 3−1+2 |
575 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18168);