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Elements of the group are displayed as permutations of degree 14.

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$D_4\times D_5\times S_5$ 1A $1$ $1$ $D_4\times D_5\times S_5$ 1A 1A 1A $()$
$D_4\times D_5\times S_5$ 2A $2$ $1$ $D_4\times D_5\times S_5$ 1A 2A 2A $(2,5)(3,4)$
$D_4\times D_5\times S_5$ 2B $2$ $2$ $C_2^2\times D_5.S_5$ 1A 2B 2B $(3,4)$
$D_4\times D_5\times S_5$ 2C $2$ $2$ $C_2^2\times D_5.S_5$ 1A 2C 2C $(2,3)(4,5)$
$D_4\times D_5\times S_5$ 2D $2$ $5$ $C_2\times D_4\times S_5$ 1A 2D 2D $(1,14)(11,13)$
$D_4\times D_5\times S_5$ 2E $2$ $5$ $C_2\times D_4\times S_5$ 1A 2E 2E $(1,14)(2,5)(3,4)(11,13)$
$D_4\times D_5\times S_5$ 2F $2$ $10$ $C_{60}:C_2^4$ 1A 2F 2F $(6,7)$
$D_4\times D_5\times S_5$ 2G $2$ $10$ $C_{60}:C_2^4$ 1A 2G 2G $(2,5)(3,4)(6,7)$
$D_4\times D_5\times S_5$ 2H $2$ $10$ $C_2^3\times S_5$ 1A 2H 2H $(1,14)(2,3)(4,5)(11,13)$
$D_4\times D_5\times S_5$ 2I $2$ $10$ $C_2^3\times S_5$ 1A 2I 2I $(1,11)(3,4)(12,13)$
$D_4\times D_5\times S_5$ 2J $2$ $15$ $D_5\times D_4^2$ 1A 2J 2J $(7,9)(8,10)$
$D_4\times D_5\times S_5$ 2K $2$ $15$ $D_5\times D_4^2$ 1A 2K 2K $(2,5)(3,4)(7,8)(9,10)$
$D_4\times D_5\times S_5$ 2L $2$ $20$ $C_{15}:C_2^5$ 1A 2L 2L $(3,4)(6,7)$
$D_4\times D_5\times S_5$ 2M $2$ $20$ $C_{15}:C_2^5$ 1A 2M 2M $(2,3)(4,5)(6,7)$
$D_4\times D_5\times S_5$ 2N $2$ $30$ $C_{20}:C_2^4$ 1A 2N 2N $(3,4)(7,8)(9,10)$
$D_4\times D_5\times S_5$ 2O $2$ $30$ $C_{20}:C_2^4$ 1A 2O 2O $(2,3)(4,5)(7,8)(9,10)$
$D_4\times D_5\times S_5$ 2P $2$ $50$ $C_{12}:C_2^4$ 1A 2P 2P $(8,10)(11,12)(13,14)$
$D_4\times D_5\times S_5$ 2Q $2$ $50$ $C_{12}:C_2^4$ 1A 2Q 2Q $(2,5)(3,4)(8,10)(11,12)(13,14)$
$D_4\times D_5\times S_5$ 2R $2$ $75$ $C_2\times D_4^2$ 1A 2R 2R $(7,8)(9,10)(11,12)(13,14)$
$D_4\times D_5\times S_5$ 2S $2$ $75$ $C_2\times D_4^2$ 1A 2S 2S $(2,5)(3,4)(7,8)(9,10)(11,12)(13,14)$
$D_4\times D_5\times S_5$ 2T $2$ $100$ $C_2^3\times D_6$ 1A 2T 2T $(1,11)(2,5)(6,8)(12,13)$
$D_4\times D_5\times S_5$ 2U $2$ $100$ $C_2^3\times D_6$ 1A 2U 2U $(1,13)(2,3)(4,5)(8,10)(12,14)$
$D_4\times D_5\times S_5$ 2V $2$ $150$ $D_4\times C_2^3$ 1A 2V 2V $(1,11)(2,3)(4,5)(7,8)(9,10)(12,13)$
$D_4\times D_5\times S_5$ 2W $2$ $150$ $D_4\times C_2^3$ 1A 2W 2W $(1,14)(2,5)(6,10)(8,9)(11,13)$
$D_4\times D_5\times S_5$ 3A $3$ $20$ $C_{60}:C_2^3$ 3A 1A 3A $(8,9,10)$
$D_4\times D_5\times S_5$ 4A $4$ $2$ $(C_4\times D_5).S_5$ 2A 4A 4A $(2,3,5,4)$
$D_4\times D_5\times S_5$ 4B $4$ $10$ $C_2\times C_4\times S_5$ 2A 4B 4B $(1,13)(2,4,5,3)(12,14)$
$D_4\times D_5\times S_5$ 4C $4$ $20$ $C_{60}:C_2^3$ 2A 4C 4C $(2,4,5,3)(6,7)$
$D_4\times D_5\times S_5$ 4D $4$ $30$ $C_4^2:D_{10}$ 2J 4D 4D $(7,8,9,10)$
$D_4\times D_5\times S_5$ 4E $4$ $30$ $C_4^2:D_{10}$ 2A 4E 4E $(2,3,5,4)(7,8)(9,10)$
$D_4\times D_5\times S_5$ 4F $4$ $30$ $C_4^2:D_{10}$ 2J 4F 4F $(2,5)(3,4)(7,8,9,10)$
$D_4\times D_5\times S_5$ 4G $4$ $60$ $C_{20}:C_2^3$ 2J 4G 4G $(2,5)(6,7,8,10)$
$D_4\times D_5\times S_5$ 4H $4$ $60$ $C_{20}:C_2^3$ 2J 4H 4H $(2,3)(4,5)(6,10,8,9)$
$D_4\times D_5\times S_5$ 4I $4$ $60$ $D_5\times C_4^2$ 2K 4I 4I $(2,3,5,4)(6,10,9,8)$
$D_4\times D_5\times S_5$ 4J $4$ $100$ $C_{12}:C_2^3$ 2A 4J 4J $(1,11)(2,4,5,3)(6,8)(12,13)$
$D_4\times D_5\times S_5$ 4K $4$ $150$ $C_4^2:C_2^2$ 2A 4K 4K $(2,4,5,3)(6,8)(9,10)(11,12)(13,14)$
$D_4\times D_5\times S_5$ 4L $4$ $150$ $C_4^2:C_2^2$ 2J 4L 4L $(1,14)(2,5)(3,4)(6,10,8,9)(11,13)$
$D_4\times D_5\times S_5$ 4M $4$ $150$ $C_4^2:C_2^2$ 2J 4M 4M $(1,13)(6,9,10,8)(12,14)$
$D_4\times D_5\times S_5$ 4N $4$ $300$ $C_2^3\times C_4$ 2J 4N 4N $(1,11)(2,5)(6,7,10,8)(12,13)$
$D_4\times D_5\times S_5$ 4O $4$ $300$ $C_2\times C_4^2$ 2K 4O 4O $(1,12)(2,4,5,3)(7,10,8,9)(11,14)$
$D_4\times D_5\times S_5$ 4P $4$ $300$ $C_2^3\times C_4$ 2J 4P 4P $(1,14)(2,3)(4,5)(6,7,8,9)(11,13)$
$D_4\times D_5\times S_5$ 5A1 $5$ $2$ $(C_5\times D_4).S_5$ 5A2 5A2 1A $(1,13,12,11,14)$
$D_4\times D_5\times S_5$ 5A2 $5$ $2$ $(C_5\times D_4).S_5$ 5A1 5A1 1A $(1,12,14,13,11)$
$D_4\times D_5\times S_5$ 5B $5$ $24$ $C_{20}:D_{10}$ 5B 5B 1A $(6,8,10,7,9)$
$D_4\times D_5\times S_5$ 5C1 $5$ $48$ $D_4\times C_5^2$ 5C2 5C2 1A $(1,13,12,11,14)(6,8,10,7,9)$
$D_4\times D_5\times S_5$ 5C2 $5$ $48$ $D_4\times C_5^2$ 5C1 5C1 1A $(1,12,14,13,11)(6,10,9,8,7)$
$D_4\times D_5\times S_5$ 6A $6$ $20$ $C_{60}:C_2^3$ 3A 2F 6A $(6,7)(8,10,9)$
$D_4\times D_5\times S_5$ 6B $6$ $20$ $C_{60}:C_2^3$ 3A 2G 6B $(2,5)(3,4)(6,7)(8,10,9)$
$D_4\times D_5\times S_5$ 6C $6$ $20$ $C_{60}:C_2^3$ 3A 2A 6C $(2,5)(3,4)(8,9,10)$
$D_4\times D_5\times S_5$ 6D $6$ $40$ $C_{15}:C_2^4$ 3A 2B 6D $(3,4)(8,10,9)$
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