Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C33×C4 |
No aliases for this group.
| Fitting | C2×C33×C4⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ #390 |
3612 conjugacy classes of subgroups; only the 863 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 863 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=f,c^2=d,b^a=bf,c^a=ce,g^a=g^2,h^a=h^2,i^a=i^2,c^b=cf288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29693);