Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C61×#1312 ⋊ C2 |
| Sylow | C61 ⋊ #11410 |
306 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 163 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,i^a=i^60,c^b=cf,i^c=i^602560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 78599);