View source for C(2^m)xC(2^m)

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== Blocks with defect group <math>C_{2^m} \times C_{2^m}</math> for <math>m>1</math> ==

These blocks were classified them over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary|CFSG]]. The Picard groups with respect to <math>\mathcal{O}</math> follow from [[References|[BKL18]]].

{| 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(2^mx2^m,1)|M(<math>C_{2^m} \times C_{2^m}</math>,1)]] || <math>k(C_{2^m} \times C_{2^m})</math> || 1 || <math>2^{2m}</math> ||1 ||<math>1</math> ||<math>(C_{2^m} \times C_{2^m}):Aut(C_{2^m} \times C_{2^m})</math> || ||1 ||1 ||
|-
|[[M(2^mx2^m,2)|M(<math>C_{2^m} \times C_{2^m}</math>,2)]] || <math>k(C_{2^m} \times C_{2^m}):C_3</math> || 1 || <math>(2^{2m}+8)/3</math> ||3 ||<math>C_3</math> || || ||1 ||1 ||
|}