Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C13×C4⋊Q8 ⋊ C4 |
| Sylow | C13 ⋊ #1980 |
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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=f,b^2=df,c^2=e,d^2=g,b^a=bd,c^a=ce,h^a=h^8,d^b=dg,f^b=fg,h^b=h^8,h^f=h^1280 conjugacy classes — view the full character table.
| maximal subgroup of | #16781358, #16781359, #16781369, … |
| maximal normal subgroup of | #16781358, #16781359, #16781369, … |
| maximal quotient of | #16784631, #16784635, #16784638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20673);