Finite Group DatabasebetaFinite Group Databasebeta| order | 37504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #2179 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^7,293|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^155,d^b=df,f^b=fg,h^c=h^138,h^e=h^292835 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37504, 20914);