# M(32,51,27)

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M(32,51,27) - $B_0(k(J_1 \times A_5))$
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Representative: $B_0(k(J_1 \times A_5))$ $(C_2)^5$ $(C_{7}:C_3) \times C_3$ 32 15 1 See below. Yes Yes Yes $B_0(\mathcal{O}(J_1 \times A_5))$ See below. 1 No Yes M(32,51,24), M(32,51,25), M(32,51,26), M(32,51,28), M(32,51,29) Yes

## Covering blocks and covered blocks

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

If $b$ is in M(32,51,27), then $B$ is also in M(32,51,27).

## Irreducible characters

All irreducible characters have height zero.

## Cartan matrix

$\left( \begin{array}{ccccccccccccccccccccc} 32 & 16 & 16 & 16 & 8 & 8 & 16 & 16 & 16 & 8 & 8 & 8 & 8 & 8 & 8 \\ 16 & 16 & 8 & 8 & 8 & 4 & 8 & 8 & 8 & 8 & 4 & 8 & 4 & 8 & 4 \\ 16 & 8 & 16 & 8 & 4 & 8 & 8 & 8 & 8 & 4 & 8 & 4 & 8 & 4 & 8 \\ 16 & 8 & 8 & 16 & 8 & 8 & 12 & 12 & 4 & 6 & 6 & 6 & 6 & 2 & 2 \\ 8 & 8 & 4 & 8 & 8 & 4 & 6 & 6 & 2 & 6 & 3 & 6 & 3 & 2 & 1 \\ 8 & 4 & 8 & 8 & 4 & 8 & 6 & 6 & 2 & 3 & 6 & 3 & 6 & 1 & 2 \\ 16 & 8 & 8 & 12 & 6 & 6 & 16 & 8 & 8 & 8 & 4 & 4 & 8 & 4 & 4 \\ 16 & 8 & 8 & 12 & 6 & 6 & 8 & 16 & 8 & 4 & 8 & 8 & 4 & 4 & 4 \\ 16 & 8 & 8 & 4 & 2 & 2 & 8 & 8 & 16 & 4 & 4 & 4 & 4 & 8 & 8 \\ 8 & 8 & 4 & 6 & 6 & 3 & 8 & 4 & 4 & 8 & 2 & 4 & 4 & 4 & 2 \\ 8 & 4 & 8 & 6 & 3 & 6 & 4 & 8 & 4 & 2 & 8 & 4 & 4 & 2 & 4 \\ 8 & 8 & 4 & 6 & 6 & 3 & 4 & 8 & 4 & 4 & 4 & 8 & 2 & 4 & 2 \\ 8 & 4 & 8 & 6 & 3 & 6 & 8 & 4 & 4 & 4 & 4 & 2 & 8 & 2 & 4 \\ 8 & 8 & 4 & 2 & 2 & 1 & 4 & 4 & 8 & 4 & 2 & 4 & 2 & 8 & 4 \\ 8 & 4 & 8 & 2 & 1 & 2 & 4 & 4 & 8 & 2 & 4 & 2 & 4 & 4 & 8 \end{array}\right)$

## Decomposition matrix

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