Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #12607 |
494 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 128 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|a^2=e,b^2=f,c^2=e,d^2=h,f^2=g,g^2=h,b^a=bd,i^a=i^60,c^b=cg,d^b=dh,e^b=eh,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, 1095981);