Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #11413 |
250 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 102 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,d^2=f,e^2=g,g^2=h,b^a=bg,c^a=cf,e^a=eh,i^a=i^11,d^b=dh,i^b=i^50,i^d=i^60,i^e=i^60664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1093324);