Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1535 |
200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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|a^2=e,c^2=f,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^8,d^b=dg,e^b=efg,h^c=h^12,h^e=h^1268 conjugacy classes — view the full character table.
| maximal subgroup of | #16781535, #16781538, #16781540, … |
| maximal normal subgroup of | #16781535, #16781538, #16781540, … |
| maximal quotient of | #16778358, #16778367, #16778376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19995);