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No, an easy example is when $G= Z/2Z {\bf Z}/2{\bf Z} \ltimes (Z/pZ)^2 {\bf Z}/p{\bf Z})^2$ where the action is by switching the factors and $H = (Z/pZ)^2. G {\bf Z}/p{\bf Z})^2$. $G$ has 2p $2p$ 1dimrepresentations and (p^2-p)/2 $(p^2-p)/2$ 2dim representations which for big p-es $p$ is smaller than the numer number of representations for H $H$ which is p^2$p^2$. |
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No, an easy example is when G= Z/2Z \ltimes (Z/pZ)^2 where the action is by switching the factors and H = (Z/pZ)^2. G has 2p 1dimrepresentations and (p^2-p)/2 2dim representations which for big p-es is smaller than the numer of representations for H which is p^2 |
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