Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#1784 ⋊ C2 |
| Sylow | C61 ⋊ #32892 |
3580 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 3580 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,c^2=h,e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^60,e^b=eh,f^b=fh,i^b=i^60,e^c=eh1009 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 318299);