Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C61×#386 ⋊ C4 |
| Sylow | C61 ⋊ #13824 |
2390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=h,c^2=eg,d^2=gh,b^a=be,c^a=cf,i^a=i^50,d^b=de,i^c=i^50,i^d=i^11,i^g=i^60520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098312);