Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C25×C3 |
| direct product | C22×C9×C22⋊A4 |
| Fitting | C26×C9 ⋊ C3 |
| derived | C24 ⋊ C22×C3×C9 |
| Sylow | C26 ⋊ C3×C9 |
3140 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 3140 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46171);