Finite Group Databasebeta

← Group #72253325

Character table — Group #72253325

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122222244444444888888888888888888888888888888888888888888882525252540404040505050505050505050505050505050505050505050508080808080808080200200200200
order1222448888551010101010105510101010101020202020202020202020202040404040404040404040404040404040404040404040404022222244444444444488888888888810101010202020204444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11-1-1ii−i−iii−i−i-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1i−ii−i
χ611111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11-1-1−i−iii−i−iii-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−ii−ii
χ711111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1ii−i−iii−i−i-1-1-1-1-1iiii−i−i−i−i-1-111-1-111−ii−ii
χ811111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1−i−iii−i−iii-1-1-1-1-1−i−i−i−iiiii-1-111-1-111i−ii−i
χ9111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ10111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-111
χ11111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ12111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1111111-1-1
χ13111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1ii−i−iii−i−i-11111−i−i−i−iiiii11-1-1-1-111i−i−ii
χ14111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1−i−iii−i−iii-11111iiii−i−i−i−i11-1-1-1-111−iii−i
χ15111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i-11111−i−i−i−iiiii-1-11111-1-1−iii−i
χ16111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii-11111iiii−i−i−i−i-1-11111-1-1i−i−ii
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χ292-22-2002−22−222-2-2-2-22222-2-222-2-2000000000000222222−2−2−2−2−2−2222222−2−2−2−2−2−222-2-20000000002i−2i2i−2i02−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ302-22-2002−22−222-2-2-2-22222-2-222-2-2000000000000222222−2−2−2−2−2−2222222−2−2−2−2−2−222-2-2000000000−2i2i−2i2i02−22−2−i2i2−i2i2−i2i2−i2i2000000000000
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χ402-2-222-2−2i2i2i−2i22-2-222-2-222-2-2-2-222222222-2-2-2-2-2-2−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i-22-220000200000000-22i−2i−2i2i00000000000000000000
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χ442-2-22-22000022-2-222-2-222-2-2-2-222-2-2-2-2-2-2222222000000000000000000000000-22-220000-20000000020000-222-22-2-22000000000000
χ4544444444444-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-100000404000000000000000000000000-1-100-1-10000
χ4644444444444-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-100000-40-40000000000000000000000001100110000
χ474444444444-14-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1000040400000000000000000000000-1-100-1-1000000
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χ49444444-4-4-4-44-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-411111-411111-411111-4111110000040-4000000000000000000000000-1-100110000
χ50444444-4-4-4-44-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-411111-411111-411111-41111100000-4040000000000000000000000001100-1-10000
χ51444444-4-4-4-4-14-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-11-411111-411111-411111-41111000040-400000000000000000000000-1-10011000000
χ52444444-4-4-4-4-14-14-14-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-11-411111-411111-411111-411110000-404000000000000000000000001100-1-1000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.