Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#11721704 |
| Fitting | C25×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×#120 |
2360 conjugacy classes of subgroups; only the 372 normal subgroups are shown.
This group has 2360 conjugacy classes of subgroups — too many to draw. Only its 372 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#120×AGL(1,ℤ/9), #72268858, #72268918, … |
| maximal normal subgroup of | C2×#120×AGL(1,ℤ/9), #72268858, #72268918, … |
| maximal quotient of | C2×#10588922⋊C3, C2×#13143663 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19829);