Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C22⋊Q8×C61 ⋊ C2 |
| Sylow | C61 ⋊ #34514 |
2016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=f,c^2=fh,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,i^b=i^601756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 335428);