Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C8×Q8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #8643 |
454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=d,c^2=h,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^11,e^c=eh,i^f=i^60658 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1088635);