Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #7248 |
244 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=d,b^2=e,c^2=fg,d^2=fg,e^2=fgh,b^a=bc,c^a=cf,e^a=efg,f^a=fh,g^a=gh,i^a=i^60,d^b=dg,d^c=dh1720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56684);