Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C13×C16 ⋊ C4 |
| Sylow | C13 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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|a^2=d,b^2=e,d^2=f,f^2=g,c^b=cg,h^b=h^8,h^e=h^12176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777997, #16778000, #16778001, … |
| maximal normal subgroup of | #16777997, #16778000, #16778001, … |
| maximal quotient of | #16786582, #16786583, #16786595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20718);