Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Fitting | C61×#322 ⋊ C4 |
| Sylow | C61 ⋊ #8140 |
330 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 104 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=dh,d^2=g,e^2=h,b^a=bd,c^a=ch,f^a=fg,e^b=eg,i^b=i^11,i^f=i^60664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1086953);