Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2185 |
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^12161 conjugacy classes — view the full character table.
| maximal subgroup of | #15775033, #15775034, #15775044, … |
| maximal normal subgroup of | #15775033, #15775034, #15775044, … |
| maximal quotient of | #15775020, #15775364, #15776124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6426);