Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C13×C4⋊Q8 ⋊ C4 |
| Sylow | C13 ⋊ #1986 |
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 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=def,c^2=e,d^2=g,b^a=bd,c^a=ce,h^a=h^5,d^b=dg,f^b=fg,h^b=h^8,h^f=h^1280 conjugacy classes — view the full character table.
| maximal subgroup of | #16781361, #16781364, #16781366, … |
| maximal normal subgroup of | #16781361, #16781364, #16781366, … |
| maximal quotient of | #16785028, #16785030, #16785036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20686);