Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C47×#1822 ⋊ C2 |
| Sylow | C47 ⋊ #20729 |
1382 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 251 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=g,d^2=e,g^2=h,b^a=be,c^a=cf,f^a=fh,d^b=dh,g^c=gh,i^c=i^46,i^d=i^46794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 169543);