Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Sylow | C33 ⋊ #356 |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^6,3^3|a^2=d,b^2=f,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2,i^a=i^2,c^b=cf,d^b=def,d^c=df195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 12155);