Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C13×C16 ⋊ C2 |
| Sylow | C13 ⋊ #2169 |
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 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) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^12,c^b=cg,h^b=h^12440 conjugacy classes — view the full character table.
| maximal subgroup of | #15750359, #15750361, #15774629, … |
| maximal normal subgroup of | #15750359, #15750361, #15774629, … |
| maximal quotient of | #15774637, #15774708, #15774726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6343);