Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C61×Q8⋊C8 ⋊ C2 |
| Sylow | C61 ⋊ #17510 |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,c^2=g,e^2=g,f^2=h,b^a=be,e^a=eg,e^b=eg,d^c=dh,i^c=i^601750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 136450);