# M(16,10,1)

M(16,10,1) - $k(C_4 \times C_2 \times C_2)$
[[File:|250px]]
Representative: $k(C_4 \times C_2 \times C_2)$ $C_4 \times C_2 \times C_2$ $1$ 16 1 1 $\left( \begin{array}{c} 16 \\ \end{array} \right)$ Yes Yes Yes $\mathcal{O} (C_4 \times C_2 \times C_2)$ $\left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right)$ 1 $\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)$ No Yes Forms a derived equivalence class Yes M(16,10,1), M(16,10,3) (complete) M(16,10,1), M(16,10,3)[1] (complete)

These are nilpotent blocks.

## Basic algebra

Quiver: a:<1,1>, b:<1,1>, c:<1,1>

Relations w.r.t. $k$: $a^4=b^2=c^2=0$, $ab+ba=ac+ca=bc+cb=0$

## Irreducible characters

All irreducible characters have height zero.

## Notes

1. For example consider the block of $C_4 \times PSL_3(7)$ covering block number 2 of $PSL_3(7)$ in the labelling used in [1]. We have $C_4 \times PSL_3(7) \triangleleft C_4 \times PGL_3(7)$.