Finite Group Databasebeta

← Group #110994

Character table — Group #110994

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222224444444444444444448888888888888888888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-111-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111111-1-1-1-1-1-111-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ121111111111-1-1-1-1-1-111-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ131111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i
χ18111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii
χ19111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1i−ii−i-11-11−ii−ii
χ20111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-11−ii−ii1-11-1i−ii−i
χ21111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii
χ22111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i
χ23111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1−ii−ii-11-11i−ii−i
χ24111111-1-1-1-1111-1-1-1-1-1111-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-11i−ii−i1-11-1−ii−ii
χ25111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-1-11i−i−iii−i−ii-111-1
χ26111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-111-1−iii−i−iii−i1-1-11
χ27111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-111111-1-11i−i−ii−iii−i1-1-11
χ28111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-111-1−iii−ii−i−ii-111-1
χ29111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-111111-1-11−iii−ii−i−ii1-1-11
χ30111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-111-1i−i−ii−iii−i-111-1
χ31111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11-1-11−iii−i−iii−i-111-1
χ32111111-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-111-1i−i−iii−i−ii1-1-11
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χ342222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
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χ362222222222-2-2-2-2-2-2-2-222-2-2-2-2-222200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
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χ40222222-2-2-2-2-2-2-22222222-22-2-222-2-200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
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χ442222-2-222-2-222-22-2-2-2-222-22-222-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ452222-2-222-2-2-2-22-22222222-22-2-2-2-22000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ462222-2-222-2-2-2-22-22222222-22-2-2-2-220000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ472222-2-222-2-2-2-22-222-2-2-2-22-2-22222-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ482222-2-222-2-2-2-22-222-2-2-2-22-2-22222-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
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χ502222-2-2-2-22222-2-2222222-2-2-22-2-22-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ512222-2-2-2-22222-2-222-2-2-2-2-2-22-222-2200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ522222-2-2-2-22222-2-222-2-2-2-2-2-22-222-220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
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χ542222-2-2-2-222-2-222-2-222-2-222-22-22-22-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ552222-2-2-2-222-2-222-2-2-2-222222-22-22-2000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ562222-2-2-2-222-2-222-2-2-2-222222-22-22-20000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
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χ5922-2-22-22-22-22-2222-20000-2-2000000−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−200-2200-2200-2200-220000000000000000
χ6022-2-22-22-22-22-2222-20000-2-2000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22002-2002-2002-2002-20000000000000000
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χ7722-2-2-222-2-22-222-22-20000-22000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i22−2−222−2−22−222−2−222−2−2i2i00−2i2i002i−2i002i−2i000000000000000000
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χ908-88-800000000000000−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-880000000000008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88000000000000−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).