〈a, b | aaaa=1, aababbb=1〉

Monoid presentation of length 11

Properties

Finite non-Abelian group with 272 elements

Completion parameters

Reduction order: left-to-right b/a

Inverses of generators

a^-1 = b⁴ab⁴
b^-1 = b¹⁵

Complete rewriting system

b¹⁶ ⇒ 1
a² ⇒ bab³
aba ⇒ b⁴ab
ab²a ⇒ b⁸ab¹⁴
ab³a ⇒ b³ab⁴
ab⁴a ⇒ b¹²
ab⁵a ⇒ b¹²ab¹³
ab⁶a ⇒ b²ab⁸
ab⁷a ⇒ b¹⁵ab¹²
ab⁸a ⇒ b¹³ab¹⁵
ab⁹a ⇒ b⁷ab⁶
ab¹⁰a ⇒ b⁹ab⁵
ab¹¹a ⇒ b⁵ab¹⁰
ab¹²a ⇒ b¹⁴ab²
ab¹³a ⇒ b⁶ab¹¹
ab¹⁴a ⇒ b¹¹ab⁷
ab¹⁵a ⇒ b¹⁰ab⁹

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 2 total

Length:	Presentation:	Description:	Related:
11	〈a, b \| aaaa=1, baabbb=a〉	Finite non-Abelian group with 272 elements
11	〈a, b \| aaaa=1, bababb=a〉	Finite non-Abelian group with 272 elements

Other isomorphic instances

4 total

Length:	Presentation:
11	〈a, b \| aaaa=1, ababbba=1〉
11	〈a, b \| aaaa=1, abbbaab=1〉
11	〈a, b \| aaaa=1, baababb=1〉
11	〈a, b \| aaaa=1, babbb=aa〉

Other anti-isomorphic instances

3 total

Length:	Presentation:
11	〈a, b \| aaaa=1, aabbbab=1〉
11	〈a, b \| aaaa=1, abaabbb=1〉
11	〈a, b \| aaaa=1, babaabb=1〉