Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C9⋊#6180 |
| derived, Sylow | C9×H(3,𝔽3) ⋊ C8 |
354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^3=h,d^a=d^2h^2,e^a=e^2,f^a=f^2,h^a=h^2,f^e=fg216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 764);