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×H(3,ℤ/4) ⋊ C4 |
| Sylow | C61 ⋊ #10888 |
762 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,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^50,e^b=eh,d^c=dh,i^c=i^11,i^f=i^60388 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1092442);