Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C22×C16×C61 ⋊ C4 |
| Sylow | C61 ⋊ #12613 |
410 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 410 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) = 3904 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=f,c^2=e,e^2=g,g^2=h,b^a=bd,f^a=fh,d^b=dh,i^b=i^11,i^f=i^601048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1096011);