#14128 ⟨a, b | aaba=b, bbbbbb=1⟩

Properties

• Presentation has sum-of-sides 11
• Finite non-Abelian group with 378 elements
• Inverses of generators:
  • a^-1 = a⁶²
  • b^-1 = b⁵

Elements

• 3 element center:
  • 1, a²¹, a⁴²
• Order of generators:
  • a: order 63
  • b: order 6
• Histogram:

  order 2	7 elements	b3, b3a9, b3a18, b3a27, b3a36, ...
  order 3	44 elements	b2, b4, b2a3, b4a3, b2a6, ...
  order 6	56 elements	b, ba3, b5, b3a3, ba6, ...
  order 7	6 elements	a9, a18, a27, a36, a45, ...
  order 9	90 elements	b2a, b2a2, b4a, b2a4, b4a2, ...
  order 18	126 elements	ba, ba2, b3a, ba4, b3a2, ...
  order 21	12 elements	a3, a6, a12, a15, a24, ...
  order 63	36 elements	a, a2, a4, a5, a8, ...

Complete rewriting system

1

# ab:aaba=b,bbbbbb=1 a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=1
ab=baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
bbbbbb=1

Right Cayley graph

Left Cayley graph

Others with same cardinality