Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#5835⋊C3 |
| unambiguous semidirect product | #5835⋊C32 |
| unambiguous semidirect product | (C3×#5835)⋊C3 |
472 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | #72253022 |
| maximal quotient of | #72253017 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39196);