Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #388 |
1045 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|b^2=e,c^2=d,b^a=bf,c^a=ce,g^a=g^2,h^a=h^2,c^b=ce,h^g=hi164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 10434);