Charles Eaton at 10:22, 13 August 2019

2019-08-13T10:22:44Z

Charles Eaton: Created page with " == Blocks with defect group $C_8 \times C_2$ == ${\rm Aut}(C_8 \times C_2)$ is a $2$ -group and $C_8 \times C_2$ is abelian, so th..."

2018-10-05T07:47:42Z

Created page with " == Blocks with defect group <math>C_8 \times C_2</math> == <math>{\rm Aut}(C_8 \times C_2)</math> is a <math>2</math>-group and <math>C_8 \times C_2</math> is abelian, so th..."

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== Blocks with defect group <math>C_8 \times C_2</math> ==

<math>{\rm Aut}(C_8 \times C_2)</math> is a <math>2</math>-group and <math>C_8 \times C_2</math> is abelian, so there is only one possible [[Glossary#Fusion system|fusion system]]. Hence every block with this defect group is nilpotent.

There is a unique <math>\mathcal{O}</math>-Morita equivalence class.

{| class="wikitable"
|-
! scope="col"| Class
! scope="col"| Representative
! scope="col"| # lifts / <math>\mathcal{O}</math>
! scope="col"| <math>k(B)</math>
! scope="col"| <math>l(B)</math>
! scope="col"| Inertial quotients
! scope="col"| <math>{\rm Pic}_\mathcal{O}(B)</math>
! scope="col"| <math>{\rm Pic}_k(B)</math>
! scope="col"| <math>{\rm mf_\mathcal{O}(B)}</math>
! scope="col"| <math>{\rm mf_k(B)}</math>
! scope="col"| Notes

|-
|[[M(16,5,1)]] || <math>k(C_8 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_8 \times C_2):{\rm Aut}(C_8 \times C_2)</math> || ||1 ||1 ||
|}

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	== Blocks with defect group <math>C_8 \times C_2</math> ==		== Blocks with defect group <math>C_8 \times C_2</math> ==

C8xC2 - Revision history

Charles Eaton at 10:22, 13 August 2019

Charles Eaton: Created page with " == Blocks with defect group C_8 \times C_2 == {\rm Aut}(C_8 \times C_2) is a 2-group and C_8 \times C_2 is abelian, so th..."

Charles Eaton: Created page with " == Blocks with defect group $C_8 \times C_2$ == ${\rm Aut}(C_8 \times C_2)$ is a $2$ -group and $C_8 \times C_2$ is abelian, so th..."