Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C43 |
No aliases for this group.
| Fitting | C4×#97×C61 ⋊ C2 |
| Sylow | C61 ⋊ #33306 |
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 331 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|b^2=e,c^2=f,d^2=gh,e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^60,c^b=ch2452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 322113);