Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1381 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^8,h^d=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | #16777894, #16777895, #16777896, … |
| maximal normal subgroup of | #16777894, #16777895, #16777896, … |
| maximal quotient of | #16777137, #16777196, #16777359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19570);