Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1318 |
170 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^8,c^b=cg,d^b=deg,d^c=dg,h^d=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | #16777722, #16777723, #16777790, … |
| maximal normal subgroup of | #16777722, #16777723, #16777790, … |
| maximal quotient of | #16776923, #16776931, #16777014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19438);