Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C47×D4⋊C8 ⋊ C2 |
| Sylow | C47 ⋊ #10457 |
460 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|c^2=dh,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fg,i^a=i^46,c^b=cf,d^b=dg,e^b=eg,e^c=egh,f^c=fg,i^c=i^461328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 73254);