Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C3×#10595527 |
| Fitting | C24×C33 ⋊ C22 |
| Sylow | C33 ⋊ C2×#120 |
3790 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 3790 conjugacy classes of subgroups — too many to draw. Only its 344 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | #72220105, C3×#11865254, D3×#10595527, … |
| maximal normal subgroup of | C3×#11865254, D3×#10595527, C3×#10595527⋊C3, … |
| maximal quotient of | #72220105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 41187);