Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×#103×C61 ⋊ C2 |
| Sylow | C61 ⋊ #25629 |
1178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|b^2=h,c^2=f,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^60,c^b=cg,f^b=fh,g^b=gh1732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 223390);