Finite Group Databasebeta

← Group #360293

Character table — Group #360293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444222244444444444444448888888888888888444444444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ17111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-111-1-111-1-11-111-1-1ii−i−iii−i−ii−ii−i
χ18111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-111-1-111-1-11-111-1-1−i−iii−i−iii−ii−ii
χ19111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-1-1-111-1-1111-1-1-111ii−i−iii−i−i−ii−ii
χ20111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-1-1-111-1-1111-1-1-111−i−iii−i−iiii−ii−i
χ21111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-1111-1-1-1-111-11-1-111−i−iii−i−iii−ii−ii
χ22111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-1111-1-1-1-111-11-1-111ii−i−iii−i−ii−ii−i
χ23111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-1-11111-1-1-1111-1-1−i−iii−i−iiii−ii−i
χ24111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-1-11111-1-1-1111-1-1ii−i−iii−i−i−ii−ii
χ25111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-11-1-111-1-1111-111-1-1−i−iiiii−i−ii−i−ii
χ26111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-11-1-111-1-1111-111-1-1ii−i−i−i−iii−iii−i
χ27111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1111-1-111-1-11-1-1-111−i−iiiii−i−i−iii−i
χ28111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1111-1-111-1-11-1-1-111ii−i−i−i−iiii−i−ii
χ29111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-1-11111-1-1-11-1-111ii−i−i−i−iii−iii−i
χ30111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-1-11111-1-1-11-1-111−i−iiiii−i−ii−i−ii
χ31111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-111-1-1-1-111-1111-1-1ii−i−i−i−iiii−i−ii
χ32111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-111-1-1-1-111-1111-1-1−i−iiiii−i−i−iii−i
χ33222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-200000000-2-20000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002200000000220000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000002200000000-2-20000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000-2-200000000220000000000000000
χ3722222-2-2-2-222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-22-2-22000000002i−2i2i−2i000000000000000000000000000000000000002i−2i2i−2i002-22-2000000000000
χ3822222-2-2-2-222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-22-2-22000000002i−2i2i−2i00000000000000000000000000000000000000−2i2i−2i2i00-22-22000000000000
χ3922222-2-2-2-222-2-2-2-222i2i−2i−2i2i2i−2i−2i-2-222-222-200000000−2i2i−2i2i22-2-222-2-2000000000000000000000000002i−2i2i−2i0000000000000000000000
χ4022222-2-2-2-222-2-2-2-222i2i−2i−2i2i2i−2i−2i-2-222-222-200000000−2i2i−2i2i-2-222-2-22200000000000000000000000000−2i2i−2i2i0000000000000000000000
χ4122222-2-2-2-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-22-2-2200000000−2i2i−2i2i000000000000000000000000000000000000002i−2i2i−2i00-22-22000000000000
χ4222222-2-2-2-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-22-2-2200000000−2i2i−2i2i00000000000000000000000000000000000000−2i2i−2i2i002-22-2000000000000
χ4322222-2-2-2-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i-2-222-222-2000000002i−2i2i−2i22-2-222-2-200000000000000000000000000−2i2i−2i2i0000000000000000000000
χ4422222-2-2-2-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i-2-222-222-2000000002i−2i2i−2i-2-222-2-222000000000000000000000000002i−2i2i−2i0000000000000000000000
χ45222-2-222-2-2-2-222-2-222i2i−2i−2i−2i−2i2i2i22-2-2-222-2000000002i−2i−2i2i000000000000000000000000000000000000002i−2i−2i2i002-2-22000000000000
χ46222-2-222-2-2-2-222-2-222i2i−2i−2i−2i−2i2i2i22-2-2-222-2000000002i−2i−2i2i00000000000000000000000000000000000000−2i2i2i−2i00-222-2000000000000
χ47222-2-222-2-2-2-222-2-222i2i−2i−2i−2i−2i2i2i-2-2222-2-2200000000−2i2i2i−2i22-2-2-2-222000000000000000000000000002i−2i−2i2i0000000000000000000000
χ48222-2-222-2-2-2-222-2-222i2i−2i−2i−2i−2i2i2i-2-2222-2-2200000000−2i2i2i−2i-2-22222-2-200000000000000000000000000−2i2i2i−2i0000000000000000000000
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χ50222-2-222-2-2-2-222-2-22−2i−2i2i2i2i2i−2i−2i22-2-2-222-200000000−2i2i2i−2i00000000000000000000000000000000000000−2i2i2i−2i002-2-22000000000000
χ51222-2-222-2-2-2-222-2-22−2i−2i2i2i2i2i−2i−2i-2-2222-2-22000000002i−2i−2i2i22-2-2-2-22200000000000000000000000000−2i2i2i−2i0000000000000000000000
χ52222-2-222-2-2-2-222-2-22−2i−2i2i2i2i2i−2i−2i-2-2222-2-22000000002i−2i−2i2i-2-22222-2-2000000000000000000000000002i−2i−2i2i0000000000000000000000
χ53222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-22200000000000000000000000000000000-2200000000-220000000000000000
χ54222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-222000000000000000000000000000000002-2000000002-20000000000000000
χ55222-2-2-2-222-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-2000000000000000000000000000000002-200000000-220000000000000000
χ56222-2-2-2-222-2-2-2-2222-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-200000000000000000000000000000000-22000000002-20000000000000000
χ5722-22-22-2-2-22-22-222-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000000000002−22−2i2−i2i2−i20000
χ5822-22-22-2-2-22-22-222-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000000000−22−22−i2i2−i2i20000
χ5922-22-22-2-2-22-22-222-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000000000−22−22−i2i2−i2i20000
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χ6122-22-22-2-2-22-22-222-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000000000−22−22i2−i2i2−i20000
χ6222-22-22-2-2-22-22-222-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000000000002−22−2−i2i2−i2i20000
χ6322-22-22-2-2-22-22-222-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000000000002−22−2−i2i2−i2i20000
χ6422-22-22-2-2-22-22-222-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000000000−22−22i2−i2i2−i20000
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χ7222-2-22-22-2-2-22-2222-2−2i2i−2i2i2i−2i2i−2i00000000-222-22i−2i−2i2i000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i22−2−220000
χ732-2-22-2222-2-22-2-22-22000000002-22-222-2-20000000000002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i00000000000000000000000000000000
χ742-2-22-2222-2-22-2-22-22000000002-22-222-2-20000000000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000000000000000
χ752-2-22-2222-2-22-2-22-22000000002-22-222-2-2000000000000-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i00000000000000000000000000000000
χ762-2-22-2222-2-22-2-22-22000000002-22-222-2-2000000000000-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i00000000000000000000000000000000
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χ782-2-22-2-2-2-22-2222-22200000000-222-2-22-220000000000002-2-222-2-2200000000-22-22-22-220000-22-220000000000000000000000000000
χ792-2-22-2-2-2-22-2222-22200000000-222-2-22-22000000000000-222-2-222-2000000002-22-22-22-20000-22-220000000000000000000000000000
χ802-2-22-2-2-2-22-2222-22200000000-222-2-22-22000000000000-222-2-222-200000000-22-22-22-2200002-22-20000000000000000000000000000
χ812-2-2-2222-222-2-2-2-22200000000-222-22-22-20000000000002-2-22-222-2000000002i−2i2i−2i−2i2i−2i2i00002i−2i−2i2i0000000000000000000000000000
χ822-2-2-2222-222-2-2-2-22200000000-222-22-22-20000000000002-2-22-222-200000000−2i2i−2i2i2i−2i2i−2i0000−2i2i2i−2i0000000000000000000000000000
χ832-2-2-2222-222-2-2-2-22200000000-222-22-22-2000000000000-222-22-2-22000000002i−2i2i−2i−2i2i−2i2i0000−2i2i2i−2i0000000000000000000000000000
χ842-2-2-2222-222-2-2-2-22200000000-222-22-22-2000000000000-222-22-2-2200000000−2i2i−2i2i2i−2i2i−2i00002i−2i−2i2i0000000000000000000000000000
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χ872-2-2-22-2-22-22-2222-22000000002-22-2-2-222000000000000-22-222-22-22-22-2-22-2200000000-222-200000000000000000000000000000000
χ882-2-2-22-2-22-22-2222-22000000002-22-2-2-222000000000000-22-222-22-2-22-222-22-2000000002-2-2200000000000000000000000000000000
χ8944-44-4-44444-4-44-4-4-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-44444-4-44-4-4-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-444-444-4-4-4-44-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-444-444-444-4-4-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ934-44444-4-44-4-4-444-4-400000000000000000000000000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ944-44444-4-44-4-4-444-4-4000000000000000000000000000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ954-4444-444-4-4-44-4-44-40000000000000000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ964-4444-444-4-4-44-4-44-400000000000000000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ974-44-4-44-44-444-44-44-4000000000000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ984-44-4-44-44-444-44-44-400000000000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ994-44-4-4-44-44444-44-4-40000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ1004-44-4-4-44-44444-44-4-4000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ1014-4-44-4444-4-44-4-44-4400000000-44-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-4-4-4-44-4444-444000000004-4-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4444-444-4-4-4-444000000004-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-44-4-44-44-4444-4400000000-44-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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