Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C61×#376 ⋊ C4 |
| Sylow | C61 ⋊ #13856 |
1774 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 432 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=h,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,i^a=i^11,c^b=cg,i^h=i^60688 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098351);