Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×C4⋊(C3⋊(C3⋊S4)) |
| Fitting | C23×C32×C4 ⋊ D3 |
2262 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 2262 conjugacy classes of subgroups — too many to draw. Only its 283 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47458);