Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×C32×D4×A4 |
| unambiguous semidirect product | C4⋊(C22×C32×A4) |
| unambiguous semidirect product | (C23×D4)⋊C33 |
| unambiguous semidirect product | (C23×C3×D4)⋊C32 |
| Fitting | C23×C32×D4 ⋊ C3 |
| Sylow | C23×D4 ⋊ C33 |
2766 conjugacy classes of subgroups; only the 646 normal subgroups are shown.
This group has 2766 conjugacy classes of subgroups — too many to draw. Only its 646 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47760);