Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #13146 |
312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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,c^2=d,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^46,i^b=i^46,e^c=eh,i^c=i^46788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 87480);