Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C61×#1959 ⋊ C2 |
| Sylow | C61 ⋊ #21199 |
1622 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=eg,c^2=f,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,c^b=ch,i^d=i^601024 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 173224);