M(16,10,2)

M(16,10,2) - [math]B_0(k(C_4 \times A_5))[/math]

Representative:	[math]B_0(k(C_4 \times A_5))[/math]
Defect groups:	[math]C_4 \times C_2 \times C_2[/math]
Inertial quotients:	[math]C_3[/math]
[math]k(B)=[/math]	16
[math]l(B)=[/math]	3
[math]{\rm mf}_k(B)=[/math]	1
[math]{\rm Pic}_k(B)=[/math]
Cartan matrix:	[math]\left( \begin{array}{ccc} 8 & 8 & 4 \\ 8 & 16 & 8 \\ 4 & 8 & 8 \\ \end{array} \right)[/math]
Defect group Morita invariant?	Yes
Inertial quotient Morita invariant?	Yes
[math]\mathcal{O}[/math]-Morita classes known?	Yes
[math]\mathcal{O}[/math]-Morita classes:	[math]B_0(\mathcal{O}(C_4\times A_5))[/math]
Decomposition matrices:	[math]\left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{array}\right)[/math]
[math]{\rm mf}_\mathcal{O}(B)=[/math]	1
[math]{\rm Pic}_{\mathcal{O}}(B)=[/math]	[math]D_8 \times C_2[/math]
[math]PI(B)=[/math]	[math]D_8 \times S_4 \times C_2[/math]
Source algebras known?	No
Source algebra reps:
[math]k[/math]-derived equiv. classes known?	Yes
[math]k[/math]-derived equivalent to:	M(16,10,3)
[math]\mathcal{O}[/math]-derived equiv. classes known?	Yes
[math]p'[/math]-index covering blocks:
[math]p'[/math]-index covered blocks:
Index [math]p[/math] covering blocks:

Basic algebra

Quiver: a:<1,2>, b:<2,3>, c:<3,2>, d:<2,1>, e:<1,1>, f: <2,2>, g:<3,3>

Relations w.r.t. [math]k[/math]: [math]ad=cb=0[/math], [math]bcda=dabc[/math], [math]e^4=f^4=g^4=0[/math], [math]af=ea[/math], [math]bg=fb[/math], [math]cf=gc[/math], [math]de=fd[/math]

Irreducible characters

All irreducible characters have height zero.

Back to [math]C_4 \times C_2 \times C_2[/math]