Finite Group Databasebeta

← Group #364445

Character table — Group #364445

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222222222222244444444444444444444444444444444222222222222444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ141111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ161111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ17111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ18111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i11-1-111-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii-1-111-1-111−i−iii−i−iii
χ19111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i-1-111-1-11111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111-1-111−i−iii−i−iii
χ20111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ21111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ22111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii11-1-111-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i-1-111-1-111ii−i−iii−i−i
χ23111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii-1-111-1-11111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii-1-111-1-111ii−i−iii−i−i
χ24111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ25111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−iii11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ26111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−iii11-1-1-1-111-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii-1-11111-1-1−i−iiiii−i−i
χ27111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−iii-1-11111-1-111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1−i−iiiii−i−i
χ28111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ29111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iii−i−i11-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ30111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iii−i−i11-1-1-1-111-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1ii−i−i−i−iii
χ31111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iii−i−i-1-11111-1-111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii-1-11111-1-1ii−i−i−i−iii
χ32111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ33222222222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222000000000000000000000000000000000000000000000000
χ37222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ38222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ39222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2222i2i2i2i−2i−2i−2i−2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ40222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222−2i−2i−2i−2i2i2i2i2i-2-22222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ41222-2-2-2222-22-22-2-2-2000000002-22-22i2i−2i−2i2i2i−2i−2i2-22-200002i−2i2i−2i0000000000002-22-200000000000000002i−2i2i−2i00000000000000000000
χ42222-2-2-2222-22-22-2-2-2000000002-22-22i2i−2i−2i2i2i−2i−2i2-22-200002i−2i2i−2i000000000000-22-220000000000000000−2i2i−2i2i00000000000000000000
χ43222-2-2-2222-22-22-2-2-2000000002-22-2−2i−2i2i2i−2i−2i2i2i2-22-20000−2i2i−2i2i0000000000002-22-20000000000000000−2i2i−2i2i00000000000000000000
χ44222-2-2-2222-22-22-2-2-2000000002-22-2−2i−2i2i2i−2i−2i2i2i2-22-20000−2i2i−2i2i000000000000-22-2200000000000000002i−2i2i−2i00000000000000000000
χ45222-2-2-2222-22-22-2-2-200000000-22-222i2i−2i−2i2i2i−2i−2i-22-220000−2i2i−2i2i000000002-22-200000000000000002i−2i2i−2i000000000000000000000000
χ46222-2-2-2222-22-22-2-2-200000000-22-222i2i−2i−2i2i2i−2i−2i-22-220000−2i2i−2i2i00000000-22-220000000000000000−2i2i−2i2i000000000000000000000000
χ47222-2-2-2222-22-22-2-2-200000000-22-22−2i−2i2i2i−2i−2i2i2i-22-2200002i−2i2i−2i000000002-22-20000000000000000−2i2i−2i2i000000000000000000000000
χ48222-2-2-2222-22-22-2-2-200000000-22-22−2i−2i2i2i−2i−2i2i2i-22-2200002i−2i2i−2i00000000-22-2200000000000000002i−2i2i−2i000000000000000000000000
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χ56222-2-2-2-2-2-222-2-222200000000-222-2-2-22222-2-2-222-200002-2-2200000000-222-200000000000000002-2-22000000000000000000000000
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χ5822-22-2-222-22-22-22-2-222-2-222-2-200002i−2i2i−2i2i−2i2i−2i00000000000000002i−2i2i−2i00000000000000000000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2
χ5922-22-2-222-22-22-22-2-222-2-222-2-20000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i000000000000000000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2
χ6022-22-2-222-22-22-22-2-222-2-222-2-20000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i00000000000000000000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2
χ6122-22-2-222-22-22-22-2-2-2-222-2-22200002i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i000000000000000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2
χ6222-22-2-222-22-22-22-2-2-2-222-2-22200002i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i00000000000000000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2
χ6322-22-2-222-22-22-22-2-2-2-222-2-2220000−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i000000000000000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2
χ6422-22-2-222-22-22-22-2-2-2-222-2-2220000−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i00000000000000000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2
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χ6622-22-2-2-2-22-2-222-22222-2-2-2-22200002-22-2-22-2200000000000000002-2-2200000000000000000000000000000000−222−2−222−2−222−2−222−2
χ6722-22-2-2-2-22-2-222-22222-2-2-2-2220000-22-222-22-20000000000000000-222-2000000000000000000000000000000002−2−222−2−22−222−2−222−2
χ6822-22-2-2-2-22-2-222-22222-2-2-2-2220000-22-222-22-20000000000000000-222-200000000000000000000000000000000−222−2−222−22−2−222−2−22
χ6922-22-2-2-2-22-2-222-222-2-22222-2-200002-22-2-22-220000000000000000-222-2000000000000000000000000000000002−2−22−222−22−2−22−222−2
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χ1024-4-44-444-44-44-4-44-4400000000-44-44000000004-44-40000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-44-44-444-44-44-4000000004-4-4400000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-44-44-444-44-44-400000000-444-4000000004-4-440000000000000000000000000000000000000000000000000000000000000000

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