M(8,5,3)

M(8,5,3) - [math]k(A_4 \times C_2)[/math]

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Representative:	[math]k(A_4 \times C_2)[/math]
Defect groups:	[math]C_2 \times C_2 \times C_2[/math]
Inertial quotients:	[math]1[/math]
[math]k(B)=[/math]	8
[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} 4 & 2 & 2 \\ 2 & 4 & 2 \\ 2 & 2 & 4 \\ \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]\mathcal{O} (A_4 \times C_2)[/math]
Decomposition matrices:	[math]\left( \begin{array}{ccc} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 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]PI(B)=[/math]	{{{PIgroup}}}
Source algebras known?	No
Source algebra reps:
[math]k[/math]-derived equiv. classes known?	Yes
[math]k[/math]-derived equivalent to:	M(8,5,2)
[math]\mathcal{O}[/math]-derived equiv. classes known?	Yes
[math]p'[/math]-index covering blocks:	{{{coveringblocks}}}
[math]p'[/math]-index covered blocks:	{{{coveredblocks}}}
Index [math]p[/math] covering blocks:	{{{pcoveringblocks}}}

Basic algebra

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

Relations w.r.t. [math]k[/math]: ab=bc=ca=0, df=fe=ed=0, ad=fc, be=da, cf=eb, g^2=h^2=i^2=0, ah=ga, bi=hb, cg=ic, dg=hd, eh=ie, fi=gf

Irreducible characters

All irreducible characters have height zero.

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