Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C61×#423 ⋊ C4 |
| Sylow | C61 ⋊ #10894 |
722 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,c^2=f,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dh,e^b=eh,i^b=i^11,d^c=dh,i^g=i^60484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1092456);