Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×D9)⋊SL(2,ℤ/4) |
551 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^4,3^3,2^2|b^2=c,f^3=g,b^a=bd,f^a=f^2g^2,g^a=g^2,e^b=e^2,h^b=hi,h^e=i,i^e=hi108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 12319);