Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C47×#2143 ⋊ C2 |
| Sylow | C47 ⋊ #13027 |
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|a^2=f,b^2=dfg,d^2=g,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^46,d^c=dg,e^c=eg,f^c=fg,g^c=gh782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 86728);