Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#1980 ⋊ C2 |
| Sylow | C47 ⋊ #10004 |
692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fh,c^b=cf,d^b=dg,i^b=i^46,d^c=dh,e^c=egh,i^c=i^46908 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 70353);