Finite Group Databasebeta

← Group #358136

Character table — Group #358136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444442222444444444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ141111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ161111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ17111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ18111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ19111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ20111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ21111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ22111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ23111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ24111-1-1-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ25111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ26111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ27111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ28111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ29111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ30111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ31111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ32111-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
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χ38222-2-2-2-2-2-222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ39222-2-2-2-2-2-222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ40222-2-2-2-2-2-222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ4122-2222-2-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i22-2-22i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000000000000000000000000000000000002i−2i2i−2i2-22-2
χ4222-2222-2-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i22-2-22i2i−2i−2i2i2i−2i−2i22-2-200000000000000000000000000000000000000000000000000000000−2i2i−2i2i-22-22
χ4322-2222-2-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i-2-2220000000000000000000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ4422-2222-2-2-22-2-22-22-22i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ4522-2222-2-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000000000000000000000000000000002i−2i2i−2i-22-22
χ4622-2222-2-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000000000000000000000000000000000000000000000000000−2i2i−2i2i2-22-2
χ4722-2222-2-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i-2-2220000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ4822-2222-2-2-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000-22-222i−2i2i−2i00000000
χ4922-2-2-2-22222-2-22-2-222i2i−2i−2i−2i−2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000000000002-2-22−2i2i2i−2i
χ5022-2-2-2-22222-2-22-2-222i2i−2i−2i−2i−2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000000000000000000000000000000000000000-222-22i−2i−2i2i
χ5122-2-2-2-22222-2-22-2-222i2i−2i−2i−2i−2i2i2i-2-222−2i−2i2i2i2i2i−2i−2i22-2-20000000000000000000000000000000000000000000000002i−2i−2i2i-222-200000000
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χ5322-2-2-2-22222-2-22-2-22−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000000000002-2-222i−2i−2i2i
χ5422-2-2-2-22222-2-22-2-22−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000000000000000000000000000000000000000-222-2−2i2i2i−2i
χ5522-2-2-2-22222-2-22-2-22−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i−2i−2i2i2i22-2-20000000000000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ5622-2-2-2-22222-2-22-2-22−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i−2i−2i2i2i22-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ572-2222-22-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000002i−2i2i−2i2-22-200000000000000000000000000000000
χ582-2222-22-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000−2i2i−2i2i-22-2200000000000000000000000000000000
χ592-2222-22-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i-22-22−2i2i−2i2i−2i2i−2i2i-22-2200000000000000002i−2i2i−2i2-22-20000000000000000000000000000000000000000
χ602-2222-22-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i-22-22−2i2i−2i2i−2i2i−2i2i-22-220000000000000000−2i2i−2i2i-22-220000000000000000000000000000000000000000
χ612-2222-22-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000002i−2i2i−2i-22-2200000000000000000000000000000000
χ622-2222-22-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000−2i2i−2i2i2-22-200000000000000000000000000000000
χ632-2222-22-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i-22-222i−2i2i−2i2i−2i2i−2i-22-2200000000000000002i−2i2i−2i-22-220000000000000000000000000000000000000000
χ642-2222-22-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i-22-222i−2i2i−2i2i−2i2i−2i-22-220000000000000000−2i2i−2i2i2-22-20000000000000000000000000000000000000000
χ652-22-2-22-222-22-22-22-22i−2i2i−2i−2i2i−2i2i2-22-22i−2i2i−2i−2i2i−2i2i-22-220000000000000000000000002i−2i−2i2i2-2-2200000000000000000000000000000000
χ662-22-2-22-222-22-22-22-22i−2i2i−2i−2i2i−2i2i2-22-22i−2i2i−2i−2i2i−2i2i-22-22000000000000000000000000−2i2i2i−2i-222-200000000000000000000000000000000
χ672-22-2-22-222-22-22-22-22i−2i2i−2i−2i2i−2i2i-22-22−2i2i−2i2i2i−2i2i−2i2-22-200000000000000002i−2i−2i2i2-2-220000000000000000000000000000000000000000
χ682-22-2-22-222-22-22-22-22i−2i2i−2i−2i2i−2i2i-22-22−2i2i−2i2i2i−2i2i−2i2-22-20000000000000000−2i2i2i−2i-222-20000000000000000000000000000000000000000
χ692-22-2-22-222-22-22-22-2−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i−2i2i2i−2i2i−2i-22-220000000000000000000000002i−2i−2i2i-222-200000000000000000000000000000000
χ702-22-2-22-222-22-22-22-2−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i−2i2i2i−2i2i−2i-22-22000000000000000000000000−2i2i2i−2i2-2-2200000000000000000000000000000000
χ712-22-2-22-222-22-22-22-2−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i−2i2i−2i2i2-22-200000000000000002i−2i−2i2i-222-20000000000000000000000000000000000000000
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χ732-2-222-2-222-2-2222-2-22-2-222-2-222-2-222-2-222-2-222-2-22000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ742-2-222-2-222-2-2222-2-22-2-222-2-222-2-222-2-222-2-222-2-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ752-2-222-2-222-2-2222-2-22-2-222-2-22-222-2-222-2-222-2-222-200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ762-2-222-2-222-2-2222-2-22-2-222-2-22-222-2-222-2-222-2-222-20000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
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χ782-2-222-2-222-2-2222-2-2-222-2-222-22-2-22-222-2-222-22-2-2200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
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χ9344-44-444-44-44-4-44-4-40000000000000000000000000000000000004-44-4000000000000000000000000000000000000000000000000
χ9444-44-444-44-44-4-44-4-4000000000000000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ9544-4-44-4-44-4-44-4-44440000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ9644-4-44-4-44-4-44-4-4444000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ974-444-4-4-4-444-4-4-44440000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-4-444-4-4-4444000000000000000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ994-44-44444-44-4-4-44-4-40000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ1004-44-44444-44-4-4-44-4-4000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-4-444-4444-4-44-4000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ1024-4-44-4-444-4444-4-44-400000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ1034-4-4-444-4-44444-4-4-44000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ1044-4-4-444-4-44444-4-4-4400000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000

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