Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #13656 |
184 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,c^2=e,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ch,d^a=df,f^a=fg,g^a=gh,i^a=i^46,d^b=df,f^b=fg,g^b=gh,i^c=i^46926 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 90181);