Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D29⋊AΣL(1,𝔽16) |
| Fitting | C29×#120 ⋊ C4 |
| Sylow | C29 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^7,29|a^2=e,b^a=bd,d^a=df,f^a=fg,h^a=h^12,e^b=ef,h^c=h^28,e^d=eg,h^e=h^28124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20756);