Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C3×#3745 |
| Fitting | C22×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ C22×D8 |
2332 conjugacy classes of subgroups; only the 558 normal subgroups are shown.
This group has 2332 conjugacy classes of subgroups — too many to draw. Only its 558 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45554);