Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1379 |
136 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 66 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=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,h^a=h^8,c^b=cg,d^b=dg,h^b=h^12,h^d=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16789087, C2×#13129891, #16789092, … |
| maximal normal subgroup of | #16789087, C2×#13129891, #16789092, … |
| maximal quotient of | #16777094, #16777104, #16777113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19565);