Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×D3×GL(2,ℤ/4) |
| Fitting | C24×C32 ⋊ C2×D3 |
1262 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×A4⋊S4, D32×GL(2,ℤ/4), C3×D3×D4×S4, … |
| maximal normal subgroup of | D32×GL(2,ℤ/4), C3×D3×D4×S4, D3×#10596473 |
| maximal quotient of | D3×A4×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46793);