Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C33 ⋊ #478 |
554 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^3|a^2=e,b^2=ef,c^2=df,d^2=f,b^a=be,c^a=cd,d^a=df,i^a=i^2,c^b=cdef,d^b=df,g^b=g^2,h^c=h^2105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 22412);