Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(3,𝔽3)×#126 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #552 |
1177 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|b^2=f,c^2=e,d^2=f,c^a=cf,g^a=g^2,h^a=h^2,d^b=def,d^c=df,h^g=hi131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20318);