Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2121 |
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 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) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,b^a=bd,d^a=df,f^a=fg,h^a=h^12,c^b=cg,e^b=ef,e^d=eg155 conjugacy classes — view the full character table.
| maximal subgroup of | #15778443, #15778445, #15778447, … |
| maximal normal subgroup of | #15778443, #15778445, #15778447, … |
| maximal quotient of | #15772009, #15772097, #15772179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6156);