# M(16,14,2)

M(16,14,2) - $k(C_2 \times C_2 \times A_5)$
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Representative: $k(C_2 \times C_2 \times A_5)$ $(C_2)^4$ $C_3$ 16 3 1 $\left( \begin{array}{ccc} 16 & 8 & 8\\ 8 & 8 & 4 \\ 8 & 4 & 8 \end{array} \right)$ Yes Yes Yes $B_0(\mathcal{O} (C_2 \times C_2 \times A_5)$ See below 1 $(C_2 \times C_2):S_3 \times C_2$ No Yes M(16,14,3) Yes

## Covering blocks and covered blocks

Let $N \triangleleft G$ with $p'$-index and let $B$ be a block of $\mathcal{O} G$ covering a block $b$ of $\mathcal{O} N$.

If $b$ is in M(16,14,2), then $B$ is in M(16,14,2) or M(16,14,9).

## Projective indecomposable modules

Labelling the simple $B$-modules by $S_1, S_2, S_3$, the projective indecomposable modules have Loewy structure as follows:

$\begin{array}{ccc} \begin{array}{c} S_1 \\ S_1 S_1 S_2 S_3 \\ S_1 S_1 S_1 S_2 S_3 S_2 S_3 \\ S_1 S_1 S_1 S_1 S_2 S_3 S_2 S_3 \\ S_1 S_1 S_1 S_2 S_3 S_2 S_3 \\ S_1 S_1 S_2 S_3 \\ S_1 \\ \end{array} & \begin{array}{c} S_2 \\ S_1 S_2 S_2 \\ S_1 S_1 S_3 S_2 \\ S_1 S_1 S_3 S_3 \\ S_1 S_1 S_3 S_2 \\ S_1 S_2 S_2 \\ S_2 \\ \end{array} & \begin{array}{c} S_3 \\ S_1 S_3 S_3 \\ S_1 S_1 S_2 S_3 \\ S_1 S_1 S_2 S_2 \\ S_1 S_1 S_2 S_3 \\ S_1 S_3 S_3 \\ S_3 \\ \end{array} \end{array}$

## Irreducible characters

All irreducible characters have height zero.

## Decomposition matrix

$\left( \begin{array}{ccc} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right)$