Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #1891 |
342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^12,e^b=eg,h^b=h^12,d^c=dg,f^c=fg200 conjugacy classes — view the full character table.
| maximal subgroup of | #15778692, #15778694, #15778699, … |
| maximal normal subgroup of | #15778692, #15778694, #15778699, … |
| maximal quotient of | #15757605, #15757610, #15757615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4929);