Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #20538 |
922 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 328 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=f,b^2=g,c^2=e,f^2=h,b^a=be,d^a=de,i^a=i^11,c^b=ceh,d^b=dh,i^d=i^60,i^f=i^60520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1104198);