Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Fitting | H(3,𝔽3)×H(5,𝔽2) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #585 |
3001 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3,2,3^2|c^2=g,e^a=eg,h^a=h^2,i^a=i^2,d^b=dg,e^c=eg,h^f=hi170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31015);