Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C61×#2031 ⋊ C2 |
| Sylow | C61 ⋊ #23993 |
1152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^60,c^b=cg,e^c=eh,g^c=gh,f^d=fh,i^d=i^60820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 202103);