Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#4536 |
| Sylow | C33 ⋊ AΣL(1,𝔽16) |
1084 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 11901);