M(16,10,3)

M(16,10,3) - [math]k(C_4 \times A_4)[/math]

Representative:	[math]k(C_4 \times A_4)[/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 & 4 & 4 \\ 4 & 8 & 4 \\ 4 & 4 & 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]\mathcal{O} (C_4 \times A_4)[/math]
Decomposition matrices:	[math]\left( \begin{array}{ccc} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 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 S_3[/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(16,10,2)
[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:<3,1>, 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]: [math]ab=bc=ca=0[/math], [math]df=fe=ed=0[/math], [math]ad=fc[/math], [math]be=da[/math], [math]cf=eb[/math], [math]g^4=h^4=i^4=0[/math], [math]ah=ga[/math], [math]bi=hb[/math], [math]cg=ic[/math], [math]dg=hd[/math], [math]eh=ie[/math], [math]fi=gf[/math]

Irreducible characters

All irreducible characters have height zero.

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