Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2153 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^8,c^b=cg,h^b=h^12,h^e=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16788623, #16788624, #16788626, … |
| maximal normal subgroup of | #16788623, #16788624, #16788626, … |
| maximal quotient of | #16788655, #16788681, #16788711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20853);