Finite Group Databasebeta

← Group #360643

Character table — Group #360643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444444448888888888888888222244444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ10111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-111
χ11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ12111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ13111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ14111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ15111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ16111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ17111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−ii−ii−i
χ18111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111ii−i−iii−i−ii−ii−i−i−iii−i−iii−ii−ii
χ19111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1ii−i−iii−i−i-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111−i−iii−i−iiii−ii−iii−i−iii−i−i−ii−ii
χ20111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1−i−iii−i−iiii−ii−i−i−iii−i−iiii−ii−i
χ21111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii−i−iii−i−iii−ii−ii
χ22111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111−i−iii−i−iii−ii−iiii−i−iii−i−ii−ii−i
χ23111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1−i−iii−i−iii-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111ii−i−iii−i−i−ii−ii−i−iii−i−iiii−ii−i
χ24111-1-1-1-1-11111-11-1-111-1-1-11111-1-1-1-111-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1ii−i−iii−i−i−ii−iiii−i−iii−i−i−ii−ii
χ25111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111ii−i−i−i−iii1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiii−i−iiii−i−i−i−iiii−i−ii
χ26111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iiii−i−ii−i−iiiii−i−i−iii−i
χ27111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−iiiii−i−ii−i−iiii−i−i−i−iii−iii−i
χ28111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111ii−i−i−i−iii-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−ii−i−ii−i−iiiii−i−ii−i−ii
χ29111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111−i−iiiii−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−iii−i−i−iiiii−i−i−iii−i
χ30111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−i−iii−iii−i−i−i−iiii−i−ii
χ31111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1ii−i−i−i−iii−iii−i−i−iiiii−i−ii−i−ii
χ32111-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1111111-1-1-111−i−iiiii−i−i-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iii−iii−iii−i−i−i−iii−iii−i
χ332222222222222222-2-2-2-2-222222222-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000-2-2-2-2000000000000
χ342222222222222222-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002222000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000-2-222000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000022-2-2000000000000
χ37222222-2-2-2-2-2-2-22-220000022-2-222-2-200000002i−2i2i−2i2i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−22−22−20000
χ38222222-2-2-2-2-2-2-22-220000022-2-222-2-200000002i−2i2i−2i2i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−22−22−220000
χ39222222-2-2-2-2-2-2-22-220000022-2-222-2-20000000−2i2i−2i2i−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−22−22−220000
χ40222222-2-2-2-2-2-2-22-220000022-2-222-2-20000000−2i2i−2i2i−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000002−22−22−22−20000
χ41222222-2-2-2-2-2-2-22-2200000-2-222-2-22200000002i−2i2i−2i−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000000000002−22−2−22−220000
χ42222222-2-2-2-2-2-2-22-2200000-2-222-2-22200000002i−2i2i−2i−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−222−22−20000
χ43222222-2-2-2-2-2-2-22-2200000-2-222-2-2220000000−2i2i−2i2i2i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−222−22−20000
χ44222222-2-2-2-2-2-2-22-2200000-2-222-2-2220000000−2i2i−2i2i2i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−2−22−220000
χ45222-2-2-222-2-2-2-2222-20000022-2-2-2-22200000002-2-222-2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ46222-2-2-222-2-2-2-2222-20000022-2-2-2-22200000002-2-222-2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ47222-2-2-222-2-2-2-2222-20000022-2-2-2-2220000000-222-2-222-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ48222-2-2-222-2-2-2-2222-20000022-2-2-2-2220000000-222-2-222-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ49222-2-2-222-2-2-2-2222-200000-2-22222-2-200000002-2-22-222-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ50222-2-2-222-2-2-2-2222-200000-2-22222-2-200000002-2-22-222-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ51222-2-2-222-2-2-2-2222-200000-2-22222-2-20000000-222-22-2-2200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ52222-2-2-222-2-2-2-2222-200000-2-22222-2-20000000-222-22-2-2200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ53222-2-2-2-2-22222-22-2-2-2-22222222-2-2-2-2-2-22-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000−2i2i−2i2i000000000000
χ54222-2-2-2-2-22222-22-2-2-2-22222222-2-2-2-2-2-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000002i−2i2i−2i000000000000
χ55222-2-2-2-2-22222-22-2-2-2-2222-2-2-2-22222-2-2222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ56222-2-2-2-2-22222-22-2-2-2-2222-2-2-2-22222-2-2222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000002i−2i−2i2i000000000000
χ5722-222-22-22-22-2-2-22-22-22-2-2000000002-220000000000002i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i2i−2i2i−2i000000002-22-2000000000000000000000000
χ5822-222-22-22-22-2-2-22-22-22-2-2000000002-220000000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i−2i2i−2i2i00000000-22-22000000000000000000000000
χ5922-222-22-22-22-2-2-22-22-22-2-2000000002-22000000000000−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i2i−2i2i−2i00000000-22-22000000000000000000000000
χ6022-222-22-22-22-2-2-22-22-22-2-2000000002-22000000000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i−2i2i−2i2i000000002-22-2000000000000000000000000
χ6122-2-2-22-222-22-22-2-222-2-222000000002-2-20000000000002i2i−2i−2i−2i−2i2i2i000000002i−2i2i−2i−2i2i−2i2i000000002-2-22000000000000000000000000
χ6222-2-2-22-222-22-22-2-222-2-222000000002-2-20000000000002i2i−2i−2i−2i−2i2i2i00000000−2i2i−2i2i2i−2i2i−2i00000000-222-2000000000000000000000000
χ6322-2-2-22-222-22-22-2-222-2-222000000002-2-2000000000000−2i−2i2i2i2i2i−2i−2i000000002i−2i2i−2i−2i2i−2i2i00000000-222-2000000000000000000000000
χ6422-2-2-22-222-22-22-2-222-2-222000000002-2-2000000000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000002-2-22000000000000000000000000
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χ672-222-22-222-2-22-2-22-22-2-22-200000000-222000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000-22-220000000000000000000000000000
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χ692-22-22-22-22-2-222-2-222-22-2200000000-22-20000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000002-2-220000000000000000000000000000
χ702-22-22-22-22-2-222-2-222-22-2200000000-22-20000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000-222-20000000000000000000000000000
χ712-22-22-22-22-2-222-2-222-22-2200000000-22-2000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000-222-20000000000000000000000000000
χ722-22-22-22-22-2-222-2-222-22-2200000000-22-2000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000002-2-220000000000000000000000000000
χ732-2-22-2-2-2-222-2-2222222-2-222-22-22-22-2-2-222-22-2000000002-2-222-2-2200000000000000002-22-200000000000000000000000000000000
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χ792-2-22-2-2-2-222-2-22222-2-222-2-22-22-22-2222-22-22-2000000000000000000000000000000000000000000002-22-2-22-220000000000000000
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χ872-2-2-2222222-2-2-22-2-2-2-2-2-22-22-222-22-22222-2-22000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ882-2-2-2222222-2-2-22-2-2-2-2-2-22-22-222-22-22222-2-2200000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8944-444-44-44-44-4-4-44-4-44-44400000000-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-444-4-44-44-444-4-4-40000000000000000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ9144-444-4-44-44-444-4-4-400000000000000000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ9244-4-4-444-4-44-44-4-4440000000000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ9344-4-4-444-4-44-44-4-44400000000000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ9444-4-4-44-444-44-44-4-44-444-4-400000000-444000000000000000000000000000000000000000000000000000000000000000000000000
χ954-444-444-4-444-44-4-4-400000000000000000000000000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ964-444-444-4-444-44-4-4-4000000000000000000000000000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ974-444-44-444-4-44-4-44-4-444-44000000004-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44-44-44-44-4-444-4-44-44-44-4000000004-44000000000000000000000000000000000000000000000000000000000000000000000000
χ994-44-44-4-44-444-4-4-44400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ1004-44-44-4-44-444-4-4-444000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ1014-4-44-4-444-4-444-44-44000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-4-444-4-444-44-4400000-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-444-4-4-4-444444-4000004-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-4-4-4-444444-400000-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000

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