Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C13×C32 ⋊ C2 |
| Sylow | C13 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^12464 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C22⋊C32, C2×#13112973, #15783111, … |
| maximal normal subgroup of | D13×C22⋊C32, C2×#13112973, #15783111, … |
| maximal quotient of | #15750257, #15750317, #15750356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2647);