Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×D4×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ #585 |
2999 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|c^2=f,e^a=ef,g^a=g^2,i^a=i^2,d^b=df,h^b=h^2,i^b=i^2,d^c=df,e^c=ef,h^g=hi98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30810);