Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#117 ⋊ C4 |
| Sylow | C13 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^8,e^b=eg,h^c=h^12,h^e=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #261×H(3,ℤ/4), #16785197, #16785343, … |
| maximal normal subgroup of | #261×H(3,ℤ/4), #16785197, #16785343, … |
| maximal quotient of | #16778909, #16778911, #16778913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20180);