Finite Group Databasebeta

← Group #146421

Character table — Group #146421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order1222222222222222444444448888888888888888222244448888888816161616161616161616161616161616161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-11-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-11-11-11-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ18111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-11-11-11-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ19111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-11-11-11-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ20111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-11-11-11-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ21111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-1-11-11-11-11-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ22111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-1-11-11-11-11-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ23111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-1-11-11-11-11-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ24111-1-1-1-111-1-1111-1-11-1-111-1-111111-1-11111-1-1-1-1-1-1-11-11-11-11-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ25111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-11-1-111-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1-111-1
χ26111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-11-1-111-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-111-1-11
χ27111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-11-1-111-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-111-1-11
χ28111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-11-1-111-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1-111-1
χ29111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ30111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ31111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ32111-1-1-1-1-1-1111-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ362222222222222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ372222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ382222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ392222222-2-2-2-22-2-2-2-2222-2-2-2-22-2-2-2-2-2-222222222-2-222-2-222-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ402222222-2-2-2-22-2-2-2-2222-2-2-2-22-2-2-2-2-2-222222222-2-2-2-222-2-2222222-2-2-2-2000000000000000000000000000000000000000000000000
χ412222222-2-2-2-22-2-2-2-2-2-2-22222-2000000000000000022-2-2-2-2220000000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ422222222-2-2-2-22-2-2-2-2-2-2-22222-2000000000000000022-2-2-2-22200000000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ432222222-2-2-2-22-2-2-2-2-2-2-22222-20000000000000000-2-22222-2-20000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ442222222-2-2-2-22-2-2-2-2-2-2-22222-20000000000000000-2-22222-2-200000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ45222-2-2-2-222-2-2222-2-22-2-222-2-22-2-2-2-222-2-2-2-22222222-22-22-22-2-2-222-2-222000000000000000000000000000000000000000000000000
χ46222-2-2-2-222-2-2222-2-22-2-222-2-22-2-2-2-222-2-2-2-2222222-22-22-22-2222-2-222-2-2000000000000000000000000000000000000000000000000
χ47222-2-2-2-222-2-2222-2-2-222-2-222-200000000000000002-22-2-22-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ48222-2-2-2-222-2-2222-2-2-222-2-222-200000000000000002-22-2-22-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ49222-2-2-2-222-2-2222-2-2-222-2-222-20000000000000000-22-222-22-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ50222-2-2-2-222-2-2222-2-2-222-2-222-20000000000000000-22-222-22-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ51222-2-2-2-2-2-2222-2-2222-2-2-2-2222-2-2-2-2222222-2-2-2-2222-2-222-2-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ52222-2-2-2-2-2-2222-2-2222-2-2-2-2222-2-2-2-2222222-2-2-2-222-222-2-222-222-2-2-2-222000000000000000000000000000000000000000000000000
χ53222-2-2-2-2-2-2222-2-222-22222-2-2-200000000000000002-2-22-222-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ54222-2-2-2-2-2-2222-2-222-22222-2-2-200000000000000002-2-22-222-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ55222-2-2-2-2-2-2222-2-222-22222-2-2-20000000000000000-222-22-2-2200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ56222-2-2-2-2-2-2222-2-222-22222-2-2-20000000000000000-222-22-2-2200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ572-2-222-2-22-22-222-22-222-22-22-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−20000000000000000
χ582-2-222-2-22-22-222-22-222-22-22-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−22−22−22−22−22−22−22−220000000000000000
χ592-2-222-2-22-22-222-22-222-22-22-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−220000000000000000
χ602-2-222-2-22-22-222-22-222-22-22-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−20000000000000000
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χ622-2-222-2-22-22-222-22-2-2-22-22-22222-2-22222-2-222-2-2-2-20000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
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χ642-2-222-2-22-22-222-22-2-2-22-22-222-2-222-2-2-2-222-2-2222200000000000000000000000000000000-222-2-222-2-222-2-222-20000000000000000
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χ672-2-222-2-2-22-222-22-2222-2-22-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−20000000000000000
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χ692-2-222-2-2-22-222-22-22-2-222-22-2222-2-222-2-222-2-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ702-2-222-2-2-22-222-22-22-2-222-22-2222-2-222-2-222-2-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ712-2-222-2-2-22-222-22-22-2-222-22-22-2-222-2-222-2-222-2-222000000000000000000000000000000002-2-222-2-22-222-2-222-20000000000000000
χ722-2-222-2-2-22-222-22-22-2-222-22-22-2-222-2-222-2-222-2-22200000000000000000000000000000000-222-2-222-22-2-222-2-220000000000000000
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χ802-2-2-2-2222-2-2222-2-22-22-2-222-22-2-22222-2-22222-2-2-2-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ812-2-2-2-222-222-22-222-22-22-222-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i2−22−2−22−22−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ822-2-2-2-222-222-22-222-22-22-222-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i−22−222−22−22−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ832-2-2-2-222-222-22-222-22-22-222-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i2−22−2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ842-2-2-2-222-222-22-222-22-22-222-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i−22−222−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ852-2-2-2-222-222-22-222-2-22-22-2-22222-2-2-2-2-2-22222-2-22200000000000000002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ862-2-2-2-222-222-22-222-2-22-22-2-22222-2-2-2-2-2-22222-2-2220000000000000000-222-22-2-222-2-22-222-200000000000000000000000000000000
χ872-2-2-2-222-222-22-222-2-22-22-2-222-2-2222222-2-2-2-222-2-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ882-2-2-2-222-222-22-222-2-22-22-2-222-2-2222222-2-2-2-222-2-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ8944-44-44-4444-4-4-4-4-440000000022−2222−2222−2222−2222−2222−2222−2222−220000000000000000000000000000000000000000000000000000000000000000
χ9044-44-44-4444-4-4-4-4-4400000000−2222−2222−2222−2222−2222−2222−2222−22220000000000000000000000000000000000000000000000000000000000000000
χ9144-44-44-4-4-4-44-4444-40000000022−2222−2222−22−2222−2222−2222−222222−220000000000000000000000000000000000000000000000000000000000000000
χ9244-44-44-4-4-4-44-4444-400000000−2222−2222−222222−2222−2222−2222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4444-44-4-4-44-40000000022−2222−22−222222−2222−22−2222−2222−22220000000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4444-44-4-4-44-400000000−2222−222222−22−2222−222222−2222−2222−220000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-44-4-44-4-444-440000000022−2222−22−2222−2222−222222−2222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-44-4-44-4-444-4400000000−2222−222222−2222−2222−22−2222−222222−220000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-444-444-4-44-4-40000000022−22−222222−2222−22−222222−22−2222−22220000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-444-444-4-44-4-400000000−222222−22−2222−222222−22−222222−2222−220000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-44-44-4-4-44-4440000000022−22−222222−22−222222−22−222222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-44-44-4-4-44-44400000000−222222−22−222222−22−222222−22−222222−220000000000000000000000000000000000000000000000000000000000000000
χ1014-44-444-44-4-4-4-4-44440000000022−22−2222−222222−22−2222−222222−2222−220000000000000000000000000000000000000000000000000000000000000000
χ1024-44-444-44-4-4-4-4-444400000000−222222−2222−22−222222−2222−22−2222−22220000000000000000000000000000000000000000000000000000000000000000
χ1034-44-444-4-4444-44-4-4-40000000022−22−2222−2222−222222−2222−22−222222−220000000000000000000000000000000000000000000000000000000000000000
χ1044-44-444-4-4444-44-4-4-400000000−222222−2222−2222−22−2222−222222−22−22220000000000000000000000000000000000000000000000000000000000000000

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