M(9,2,16)

M(9,2,16) - [math]B_0(kPSL_3(4))[/math]

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Representative:	[math]B_0(kPSL_3(4))[/math]
Defect groups:	[math]C_3 \times C_3[/math]
Inertial quotients:	[math]Q_8[/math]
[math]k(B)=[/math]	6
[math]l(B)=[/math]	5
[math]{\rm mf}_k(B)=[/math]	1
[math]{\rm Pic}_k(B)=[/math]
Cartan matrix:	[math]\left( \begin{array}{ccccc} 2 & 1 & 1 & 1 & 2 \\ 1 & 2 & 1 & 1 & 2 \\ 1 & 1 & 2 & 1 & 2 \\ 1 & 1 & 1 & 5 & 4 \\ 1 & 2 & 2 & 4 & 5 \\ \end{array} \right)[/math]
Defect group Morita invariant?
Inertial quotient Morita invariant?
[math]\mathcal{O}[/math]-Morita classes known?
[math]\mathcal{O}[/math]-Morita classes:
Decomposition matrices:	[math]\left( \begin{array}{ccccc} 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 1 \\ \end{array}\right)[/math]
[math]{\rm mf}_\mathcal{O}(B)=[/math]	1
[math]{\rm Pic}_{\mathcal{O}}(B)=[/math]
[math]PI(B)=[/math]
Source algebras known?	No
Source algebra reps:
[math]k[/math]-derived equiv. classes known?	No
[math]k[/math]-derived equivalent to:
[math]\mathcal{O}[/math]-derived equiv. classes known?	No
[math]p'[/math]-index covering blocks:
[math]p'[/math]-index covered blocks:
Index [math]p[/math] covering blocks:

Basic algebra

Quiver:

Relations w.r.t. [math]k[/math]:

Other notatable representatives

[math]B_2(kO'N)[/math], [math]B_0(kPSL_3(q))[/math] for [math]q \equiv 4 \ {\rm or} \ 7 \mod 9[/math]

Irreducible characters

All irreducible characters have height zero.

Back to [math]C_3 \times C_3[/math]