〈a, b | aaaaa=1, aababb=1〉

Monoid presentation of length 11

Properties

Finite non-Abelian group with 165 elements

Completion parameters

Reduction order: left-to-right b/a

Inverses of generators

a^-1 = abab²
b^-1 = b¹⁴

Complete rewriting system

b¹⁵ ⇒ 1
b⁵a ⇒ ab⁵
ab³a ⇒ b⁴ab⁸
ab⁴a ⇒ b²ab¹¹
ba² ⇒ ab²ab¹⁴
bab²a ⇒ abab²
b³aba ⇒ a²b⁴
a³ ⇒ bab²
a²ba ⇒ b¹³
a²b²a ⇒ (ba)²b⁹
a(ba)² ⇒ b³ab²
ab(ba)² ⇒ b(ba)²b⁹

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 3 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaba=b, bbbbb=1〉	Finite non-Abelian group with 165 elements
11	〈a, b \| aabba=b, bbbbb=1〉	Finite non-Abelian group with 165 elements
11	〈a, b \| aaba=bb, bbbbb=1〉	Finite non-Abelian group with 165 elements

Other isomorphic instances

3 total

Length:	Presentation:
11	〈a, b \| aaaaa=1, ababba=1〉
11	〈a, b \| aaaaa=1, abbaab=1〉
11	〈a, b \| aaaaa=1, baabab=1〉

Other anti-isomorphic instances

2 total

Length:	Presentation:
11	〈a, b \| aaaaa=1, aabbab=1〉
11	〈a, b \| aaaaa=1, abaabb=1〉