Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C61×#1273 ⋊ C2 |
| Sylow | C61 ⋊ #10673 |
526 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 165 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=deg,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,f^b=fh,i^b=i^60,d^c=dg,e^c=eg,f^c=fh,i^c=i^602452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 74618);