Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C61×#3027 ⋊ C2 |
| Sylow | C61 ⋊ #13350 |
738 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|e^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,c^b=cf,g^b=gh,d^c=dg,e^c=eh,i^c=i^60,f^d=fh898 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 88550);