Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ C8×Q16 |
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^b=h^12,h^c=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15774645, #15774649, #15774650, … |
| maximal normal subgroup of | #15774645, #15774649, #15774650, … |
| maximal quotient of | #15753687, #15754151, #15756834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3316);