Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C61 ⋊ C8×#120 |
1786 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1786 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) = 3904 |
Polycyclic presentation:
2^8,61|a^2=g,d^2=g,g^2=h,b^a=be,c^a=cf,i^a=i^50,i^d=i^11,i^g=i^60532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1106380);