Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| unambiguous semidirect product | D61⋊#2883 |
| Fitting | C2×H(5,𝔽2)×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#2883 |
5338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=g,b^a=bf,f^a=fh,i^a=i^11,g^b=gh,d^c=dh,i^e=i^60,i^g=i^60592 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1114717);