#10664 ⟨a, b | aaaa=bbb, abab=1⟩

Properties

Presentation has sum-of-sides 11
Finite non-Abelian group with 336 elements
Inverses of generators:
- a^-1 = a⁵⁵
- b^-1 = aba

Element profile

14 element center:
- 1, a⁴, a⁸, a¹², a¹⁶, a²⁰, a²⁴, a²⁸, a³², a³⁶, a⁴⁰, a⁴⁴, a⁴⁸, a⁵²

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:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1

a⁵⁶ ⇒ 1
a⁴b ⇒ ba⁴
b² ⇒ aba⁵
bab ⇒ a⁵⁵
ba²b ⇒ a³ba⁴⁷
aba³b ⇒ ba³ba⁴³

# ab:aaaa=bbb,abab=1 a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=1
aaaab=baaaa
bb=abaaaaa
bab=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
baab=aaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
abaaab=baaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

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#10664 ⟨a, b | aaaa=bbb, abab=1⟩

Properties

Element profile

Complete rewriting system

Right Cayley graph

Left Cayley graph