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Results (23 matches)

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Elements of the group are displayed as matrices in $\GL_{5}(\F_{2})$.

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_2^4:S_4$ 1A $1$ $1$ $C_2^4:S_4$ 1A 1A $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2A $2$ $1$ $C_2^4:S_4$ 1A 2A $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2B $2$ $2$ $C_2^4:A_4$ 1A 2B $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2C $2$ $6$ $C_2^4:C_4$ 1A 2C $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2D $2$ $6$ $C_2^4:C_4$ 1A 2D $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 0 & 0 \end{array}\right) $
$C_2^4:S_4$ 2E $2$ $6$ $C_2^4:C_4$ 1A 2E $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2F $2$ $6$ $C_2^3:D_4$ 1A 2F $ \left(\begin{array}{rrrrr} 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 0 & 0 \end{array}\right) $
$C_2^4:S_4$ 2G $2$ $6$ $C_2^3:D_4$ 1A 2G $ \left(\begin{array}{rrrrr} 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2H $2$ $6$ $C_2^3:D_4$ 1A 2H $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 2I $2$ $24$ $C_2^4$ 1A 2I $ \left(\begin{array}{rrrrr} 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 \end{array}\right) $
$C_2^4:S_4$ 3A $3$ $32$ $C_2\times C_6$ 3A 1A $ \left(\begin{array}{rrrrr} 1 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 \end{array}\right) $
$C_2^4:S_4$ 4A $4$ $12$ $D_4:C_2^2$ 2A 4A $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 \end{array}\right) $
$C_2^4:S_4$ 4B $4$ $12$ $D_4:C_2^2$ 2A 4B $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 0 & 0 \end{array}\right) $
$C_2^4:S_4$ 4C $4$ $24$ $C_2^2\times C_4$ 2F 4C $ \left(\begin{array}{rrrrr} 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 \\ 1 & 1 & 1 & 1 & 1 \end{array}\right) $
$C_2^4:S_4$ 4D $4$ $24$ $C_2^2\times C_4$ 2G 4D $ \left(\begin{array}{rrrrr} 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 1 \end{array}\right) $
$C_2^4:S_4$ 4E $4$ $24$ $C_2^2\times C_4$ 2G 4E $ \left(\begin{array}{rrrrr} 0 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 1 \end{array}\right) $
$C_2^4:S_4$ 4F $4$ $24$ $C_2^2\times C_4$ 2F 4F $ \left(\begin{array}{rrrrr} 1 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 \end{array}\right) $
$C_2^4:S_4$ 4G $4$ $24$ $C_2^2\times C_4$ 2A 4G $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 \end{array}\right) $
$C_2^4:S_4$ 4H $4$ $24$ $C_2^2\times C_4$ 2H 4H $ \left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right) $
$C_2^4:S_4$ 4I $4$ $24$ $C_2^2\times C_4$ 2H 4I $ \left(\begin{array}{rrrrr} 0 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right) $
$C_2^4:S_4$ 6A $6$ $32$ $C_2\times C_6$ 3A 2A $ \left(\begin{array}{rrrrr} 0 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 6B1 $6$ $32$ $C_2\times C_6$ 3A 2B $ \left(\begin{array}{rrrrr} 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) $
$C_2^4:S_4$ 6B-1 $6$ $32$ $C_2\times C_6$ 3A 2B $ \left(\begin{array}{rrrrr} 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) $
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