Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C3 |
| unambiguous semidirect product | #10596118⋊C3 |
| Fitting | H(3,𝔽3)×C22⋊Q8 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #562 |
844 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^4,3,2^2,3^2|b^2=g,c^2=g,d^2=g,c^a=cg,d^a=dfg,h^a=h^2,i^a=i^2,c^b=cf,d^b=dg,h^e=hi113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19031);