Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C8×Q8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #20521 |
866 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,c^2=eg,d^2=ef,f^2=h,b^a=be,c^a=ch,i^a=i^50,c^b=ch,i^b=i^50,d^c=dh,i^c=i^50,i^d=i^11,i^f=i^60,i^g=i^60700 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1104124);