Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1307 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^5,c^b=cg,d^b=df,h^b=h^8,h^d=h^12,h^e=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | #16777884, #16777885, #16777940, … |
| maximal normal subgroup of | #16777884, #16777885, #16777940, … |
| maximal quotient of | #16776873, #16776875, #16776891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19416);