Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#117 ⋊ C4 |
| Sylow | C13 ⋊ C2×#339 |
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 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^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^b=h^8,h^c=h^12,h^f=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#339, #16785205, #16785222, … |
| maximal normal subgroup of | #261×#339, #16785205, #16785222, … |
| maximal quotient of | #16778965, #16778973, #16778981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20186);