Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | H(3,𝔽3)×#100 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ AΣL(1,𝔽16) |
517 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^3|b^2=c,c^2=f,b^a=bd,c^a=ce,g^a=g^2,h^a=h^2,d^b=de,e^b=ef,d^c=df,h^g=hi83 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 1843);