Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C47 ⋊ #7372 |
178 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 47 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=eg,c^2=g,d^2=f,e^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^46,c^b=ch,d^b=degh,d^c=dgh,e^d=eh764 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 56987);