Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C13×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C13 ⋊ #3036 |
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^12,f^c=fg164 conjugacy classes — view the full character table.
| maximal subgroup of | #15897487, #15897491, #15897498, … |
| maximal normal subgroup of | #15897487, #15897491, #15897498, … |
| maximal quotient of | #15846694, #15846700, #15846705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13971);