Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C61×#2252 ⋊ C2 |
| Sylow | C61 ⋊ #12503 |
306 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|b^2=df,c^2=e,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,i^a=i^60,i^c=i^601210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 84222);