Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C61×#519 ⋊ C4 |
| Sylow | C61 ⋊ #34262 |
2198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=f,c^2=h,d^2=f,e^2=g,b^a=bf,c^a=cg,e^a=ef,i^a=i^50,d^b=df,i^c=i^11,i^h=i^60598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1114373);