Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C61×#1749 ⋊ C2 |
| Sylow | C61 ⋊ #29110 |
1078 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 191 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=fg,b^2=egh,f^2=h,b^a=be,c^a=cf,d^a=deh,c^b=cg,f^c=fh,i^c=i^601726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 269104);