Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊(C3⋊(#131⋊C3)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊(#131⋊C3)) |
560 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39244);