Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | A4×C4⋊#157 |
| unambiguous semidirect product | C4⋊(A4×#157) |
| unambiguous semidirect product | (C22×C4⋊#157)⋊C3 |
| Fitting | C22×C32×C4 ⋊ C3×C4 |
382 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46729);