Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C24×C33 ⋊ C4 |
| Sylow | C33 ⋊ AΣL(1,𝔽16) |
716 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^6,3^3|a^2=c,b^a=bd,d^a=de,e^a=ef,g^a=g^2,h^a=hi,i^a=hi^2,c^b=ce,d^c=df,h^c=h^2,i^c=i^2123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23303);