Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C61×#421 ⋊ C2 |
| Sylow | C61 ⋊ #23527 |
1336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|c^2=e,e^2=h,b^a=be,c^a=cf,e^a=eh,g^a=gh,c^b=cg,e^b=eh,f^b=fh,i^b=i^60,d^c=dh,f^c=fh,g^c=gh,i^c=i^601366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 197428);