Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#473 ⋊ C4 |
| Sylow | C61 ⋊ #23042 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=eg,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^11,d^b=de,e^b=eh,g^b=gh,i^b=i^11,f^c=fh,i^d=i^60,i^g=i^60298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1111820);