Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #21657 |
802 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=fh,c^2=e,d^2=gh,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^60,c^b=ch,d^b=dh,d^c=dh2464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 177716);