Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #11884 |
510 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 103 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=gh,d^2=g,e^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^46,c^b=cfh,d^b=dg,e^b=efg,d^c=dh,e^d=eh911 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 80631);