Finite Group DatabasebetaFinite Group Databasebeta| order | 31168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #121×C487 ⋊ C2 |
| Sylow | C487 ⋊ #447 |
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7792 |
Polycyclic presentation:
2^6,487|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^b=g^4863421 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31168, 682);