Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C42×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ #383 |
423 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|a^2=d,b^2=e,c^2=f,b^a=bf,c^a=cef,g^a=gh,h^a=gh^2i^2,g^d=g^2,h^d=h^2i,h^g=hi116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13386);