Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #7604 |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=f,c^2=fgh,d^2=g,e^2=h,b^a=bd,c^a=cg,d^a=df,i^a=i^60,d^b=dg,e^b=efg1732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 57692);