Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D61⋊#1799 |
| Fitting | C2×C4×D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#1799 |
2066 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=e,b^a=be,c^a=cf,f^a=fh,i^a=i^11,g^c=gh,i^d=i^60,i^g=i^60664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1104515);