C4xC2xC2 - Revision history

Charles Eaton at 14:01, 7 October 2019

2019-10-07T14:01:07Z

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2018-12-05T08:49:32Z

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Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_4 \times C_2 \times C_2$ == These are blocks were classified over $\mathcal{O}$ in [EL18a] us..."

2018-10-04T21:30:57Z

Created page with "__NOTITLE__ == Blocks with defect group <math>C_4 \times C_2 \times C_2</math> == These are blocks were classified over <math>\mathcal{O}</math> in [EL18a] us..."

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__NOTITLE__

== Blocks with defect group <math>C_4 \times C_2 \times C_2</math> ==

These are blocks were classified over <math>\mathcal{O}</math> in [[References|[EL18a]]] using the [[Glossary#CFSG|CFSG]]. Each <math>k</math>-Morita equivalence class lifts to an 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(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || || ||1 ||1 ||
|-
|[[M(16,10,2)]] || <math>B_0(k(C_4 \times A_5))</math> || 1 ||16 ||3 ||<math>C_3</math> || || ||1 ||1 ||
|-
|[[M(16,10,3)]] || <math>k(C_4 \times A_4)</math> || 1 ||16 ||3 ||<math>C_3</math> || || ||1 ||1 ||
|}

@@ Line 20: / Line 20: @@
 |-
-|[[M(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || <math>\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)</math> || ||1 ||1 ||
+|[[M(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || <math>(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)</math> || ||1 ||1 ||
 |-
 |[[M(16,10,2)]] || <math>B_0(k(C_4 \times A_5))</math> || 1 ||16 ||3 ||<math>C_3</math> || <math>D_8 \times C_2</math> || ||1 ||1 ||

@@ Line 20: / Line 20: @@
 |-
-|[[M(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || || ||1 ||1 ||
+|[[M(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || <math>\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)</math> || ||1 ||1 ||
 |-
-|[[M(16,10,2)]] || <math>B_0(k(C_4 \times A_5))</math> || 1 ||16 ||3 ||<math>C_3</math> || || ||1 ||1 ||
+|[[M(16,10,2)]] || <math>B_0(k(C_4 \times A_5))</math> || 1 ||16 ||3 ||<math>C_3</math> || <math>D_8 \times C_2</math> || ||1 ||1 ||
 |-
-|[[M(16,10,3)]] || <math>k(C_4 \times A_4)</math> || 1 ||16 ||3 ||<math>C_3</math> || || ||1 ||1 ||
+|[[M(16,10,3)]] || <math>k(C_4 \times A_4)</math> || 1 ||16 ||3 ||<math>C_3</math> || <math>D_8 \times S_3</math>|| ||1 ||1 ||
 |}

C4xC2xC2 - Revision history

Charles Eaton at 14:01, 7 October 2019

Charles Eaton: Pic

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_4 \times C_2 \times C_2 == These are blocks were classified over \mathcal{O} in [EL18a] us..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_4 \times C_2 \times C_2$ == These are blocks were classified over $\mathcal{O}$ in [EL18a] us..."