Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C3 |
| unambiguous semidirect product | #10596184⋊C3 |
| Sylow | H(3,𝔽3) ⋊ #559 |
934 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^4,3,2^2,3^2|a^2=g,b^2=g,c^2=f,b^a=bg,d^a=df,h^a=h^2,i^a=i^2,d^b=dg,d^c=df,h^e=hi131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19335);