Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
No aliases for this group.
| Fitting | C33×C22⋊C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C4×D4 |
3084 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|d^2=e,c^a=cf,g^a=g^2,h^a=h^2,c^b=cf,i^b=i^2,d^c=df180 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×D4×C3⋊D3 |
| maximal normal subgroup of | C4×D3×D4×C3⋊D3 |
| maximal quotient of | #72268985 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 41975);