Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×#366 ⋊ C2 |
| Sylow | C13 ⋊ #1415 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=ce,e^b=ef,f^b=fg,h^b=h^12170 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1415, C2×#13113013, #15783351, … |
| maximal normal subgroup of | D13×#1415, C2×#13113013, #15783351, … |
| maximal quotient of | #15750368, #15750473, #15750551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2687);