# M(16,10,3)

M(16,10,3) - $k(C_4 \times A_4)$
Representative: $k(C_4 \times A_4)$ $C_4 \times C_2 \times C_2$ $C_3$ 16 3 1 $\left( \begin{array}{ccc} 8 & 4 & 4 \\ 4 & 8 & 4 \\ 4 & 4 & 8 \\ \end{array} \right)$ Yes Yes Yes $\mathcal{O} (C_4 \times A_4)$ $\left( \begin{array}{ccc} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{array}\right)$ 1 $D_8 \times S_3$[1] $D_8 \times S_4 \times C_2$[2] No Yes M(16,10,2) Yes

## 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. $k$: $ab=bc=ca=0$, $df=fe=ed=0$, $ad=fc$, $be=da$, $cf=eb$, $g^4=h^4=i^4=0$, $ah=ga$, $bi=hb$, $cg=ic$, $dg=hd$, $eh=ie$, $fi=gf$

## Irreducible characters

All irreducible characters have height zero.

## Notes

1. See [EL18c]
2. By Theorem 3.7 of [EL18c].