Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C29 ⋊ C4 |
| Sylow | C29 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^17,e^b=eg,h^b=h^12,h^c=h^28,h^e=h^28,h^f=h^28184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20222);