Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #14355 |
1566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|b^2=g,c^2=h,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,i^c=i^11,i^h=i^60664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098850);