Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C43 |
No aliases for this group.
| Fitting | C61×#397 ⋊ C4 |
| Sylow | C61 ⋊ #14253 |
1354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=f,c^2=ef,d^2=efgh,b^a=be,c^a=cf,d^a=de,i^a=i^50,c^b=cg,i^d=i^11,i^h=i^60406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098748);