C9xC3

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Blocks with defect group [math]C_9 \times C_3[/math]

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CLASSIFICATION INCOMPLETE
Class Representative # lifts / [math]\mathcal{O}[/math] [math]k(B)[/math] [math]l(B)[/math] Inertial quotients [math]{\rm Pic}_\mathcal{O}(B)[/math] [math]{\rm Pic}_k(B)[/math] [math]{\rm mf_\mathcal{O}(B)}[/math] [math]{\rm mf_k(B)}[/math] Notes
M(27,2,1) [math]k(C_9 \times C_3)[/math] 1 27 1 [math]1[/math] 1 1
M(27,2,2) [math]k((C_9 \times C_3):C_2)[/math] 15 2 [math]C_2[/math] 1 1 Simultaneously inverting elements of [math]C_9[/math] and [math]C_3[/math]
M(27,2,3) [math]k(D_{18} \times C_3)[/math] 18 2 [math]C_2[/math] 1 1
M(27,2,4) [math]B_0(k(SL_2(8) \times C_3))[/math] 18 2 [math]C_2[/math] 1 1
M(27,2,5) [math]k(C_9 \times S_3)[/math] 27 2 [math]C_2[/math] 1 1
M(27,2,6) [math]k(D_{18} \times S_3)[/math] 18 4 [math]C_2 \times C_2[/math] 1 1
M(27,2,7) [math]B_0(k(SL_2(8) \times S_3))[/math] 18 4 [math]C_2 \times C_2[/math] 1 1