Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1917 |
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^12,c^b=cg,h^b=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1917, C2×#13115402, #15864981, … |
| maximal normal subgroup of | D13×#1917, C2×#13115402, #15864981, … |
| maximal quotient of | #15761066, #15761073, #15761080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5076);