Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C47 ⋊ #8958 |
534 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 143 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=f,b^2=df,c^2=g,d^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^46,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg1628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 64218);