#21778 ⟨a, b | aaa=1, babbbbb=a⟩

Properties

Presentation has sum-of-sides 11
Finite non-Abelian group with 378 elements
Inverses of generators:
- a^-1 = a²
- b^-1 = b¹²⁵

Element profile

6 element center:
- 1, b²¹, b⁴², b⁶³, b⁸⁴, b¹⁰⁵

Complete rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Right-to-left recursive path with deg(b) = 0; deg(a) = 1

b¹²⁶ ⇒ 1
ab ⇒ b²⁵a
a³ ⇒ 1

# ab:aaa=1,babbbbb=a reversed:b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ab=bbbbbbbbbbbbbbbbbbbbbbbbba
aaa=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 1 total

Σ	#	Presentation	Description	Related
11	14128	⟨a, b \| aaba=b, bbbbbb=1⟩	Finite non-Abelian group with 378 elements

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