〈a, b | aabba=b, bbbbb=1〉

Monoid presentation of length 11

Properties

Finite non-Abelian group with 165 elements

Completion parameters

Reduction order: left-to-right a/b

Inverses of generators

a^-1 = a¹⁴
b^-1 = a(aba³)²

Complete rewriting system

a¹⁵ ⇒ 1
a⁵b ⇒ ba⁵
b² ⇒ a³ba⁹
bab ⇒ aba¹²
aba²b ⇒ ba⁴ba¹⁴
aba³b ⇒ (ba²)²
a³ba⁴b ⇒ ba³ba⁴
ba²ba⁴b ⇒ a¹²

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 8 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaba=b, bbbbb=1〉	Finite non-Abelian group with 165 elements
11	〈a, b \| aaba=bb, bbbbb=1〉	Finite non-Abelian group with 165 elements
11	〈a, b \| aaaaa=1, aababb=1〉	Finite non-Abelian group with 165 elements	3 isomorphic, 2 anti-isomorphic