Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | M16×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ #568 |
971 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 971 conjugacy classes of subgroups — too many to draw. Only its 193 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|d^2=e,e^2=f,c^a=cf,g^a=g^2,i^a=i^2,c^b=cf,d^b=df,h^b=h^2,i^b=i^2,d^c=df,h^g=hi104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 15939);