Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C35 |
| unambiguous semidirect product | C4⋊#92404 |
| Fitting | C4×H(5,𝔽3) ⋊ C2 |
| Sylow | H(5,𝔽3) ⋊ D4 |
2344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^3,3^5|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2,g^d=gh,f^e=fh175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3409);