Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | Q8×C4⋊C4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #34242 |
2286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=h,c^2=f,d^2=fg,e^2=g,b^a=bf,c^a=cg,e^a=ef,i^a=i^60,d^b=df,i^c=i^60,i^d=i^60,i^e=i^601588 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 330418);