Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C33 ⋊ C2×#137 |
1240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^3|b^2=f,c^2=f,d^2=ef,e^2=f,d^a=df,h^a=h^2,d^b=de,e^b=ef,g^b=g^2,d^c=de,e^c=ef,i^c=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 33822);