Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#1296 ⋊ C2 |
| Sylow | C47 ⋊ #10351 |
500 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 121 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=d,b^2=dg,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,c^b=cf,e^b=eh,f^b=fh,i^b=i^46,e^c=eg,f^c=fh,i^c=i^46920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 72594);