Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #13775 |
3566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^11,c^b=ce,i^g=i^60688 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098212);