Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C31×#462 ⋊ C2 |
| Sylow | C31 ⋊ #3299 |
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1984 |
Polycyclic presentation:
2^7,31|a^2=eg,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^30,d^b=de,h^b=h^30,f^c=fg,h^c=h^30,h^d=h^30320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 16389);