Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #13489 |
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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=eg,c^2=d,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^46,c^b=cf,f^b=fg,g^b=gh,f^c=fg,g^c=gh1052 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 89406);