Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C4×#99×C61 ⋊ C2 |
| Sylow | C61 ⋊ #12628 |
628 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=f,c^2=eh,d^2=h,b^a=bd,c^a=ch,d^a=dh,f^a=fgh,i^a=i^60,d^b=dg,g^b=gh,f^d=fh1366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 84743);