Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1315 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^8,c^b=cg,d^b=deg,h^d=h^1298 conjugacy classes — view the full character table.
| maximal subgroup of | #16777726, #16777727, #16777728, … |
| maximal normal subgroup of | #16777726, #16777727, #16777728, … |
| maximal quotient of | #16776927, #16776929, #16776931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19432);