Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #12659 |
346 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 136 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=e,b^2=f,c^2=de,f^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^60,c^b=cg,d^b=dh,i^b=i^11,f^c=fh,i^f=i^60664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1096240);