Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#10593663 |
| Fitting | C32×H(5,𝔽2) ⋊ D3 |
496 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #72252971, C2×C3×#10593663 |
| maximal normal subgroup of | C2×C3×#10593663 |
| maximal quotient of | #72252958, C2×C3×#10593663 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39094);