Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of A4×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C4×A4×#157 |
| unambiguous semidirect product | (C22×C4×#157)⋊C3 |
| Fitting | C22×C32×C4 ⋊ C3×C4 |
| derived | C22×C32 ⋊ C3×C42 |
422 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46728);