Finite Group DatabasebetaFinite Group Databasebeta| order | 37504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×M16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #2873 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^7,293|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^b=h^138,h^f=h^2921528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37504, 21073);