Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C33 |
No aliases for this group.
| Fitting | C22×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ #393 |
2828 conjugacy classes of subgroups; only the 741 normal subgroups are shown.
This group has 2828 conjugacy classes of subgroups — too many to draw. Only its 741 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|b^2=e,c^2=e,b^a=bf,c^a=cd,g^a=g^2,h^a=h^2,i^a=i^2,c^b=ce282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29934);