Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| unambiguous semidirect product | D37⋊#410 |
| Fitting | C2×#41×C37 ⋊ C4 |
| Sylow | C37 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^7,37|a^2=f,c^2=g,b^a=be,e^a=eg,h^a=h^31,f^b=fg,h^d=h^36,h^f=h^36224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 21106);