Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#1335 ⋊ C2 |
| Sylow | C47 ⋊ #12313 |
356 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 61 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=h,b^2=h,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^46,d^b=df,e^b=eg,g^b=gh,i^b=i^46,d^c=dg,e^c=eg,f^c=fh,g^c=gh1046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 82978);