Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×M32 ⋊ C4 |
| Sylow | C29 ⋊ C2×#347 |
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,d^b=dg,h^b=h^12,h^c=h^28,h^e=h^28184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20725);