Finite Group DatabasebetaFinite Group Databasebeta| order | 37504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C293 ⋊ C4 |
| Sylow | C293 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^7,293|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^155,e^b=eg,h^b=h^138,h^c=h^292,h^e=h^292,h^f=h^2921504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37504, 20222);