Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C47 ⋊ #12541 |
402 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 243 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=e,c^2=f,d^2=g,g^2=h,b^a=bg,e^a=eh,i^a=i^46,c^b=ch,d^b=dh1928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 84399);