Finite Group Databasebeta

← Group #385111

Character table — Group #385111

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111111111111111111111111444444444444444444444444444444444444444444444444888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444488888888888888888888888888888888444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ181111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ191111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ201111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ211111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iii−i−iii
χ221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111-1-11111-1-111-1-1−i−iii−i−iii−i−iiiii−i−i
χ231111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111-1-11111-1-111-1-1ii−i−iii−i−iii−i−i−i−iii
χ241111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−iii−i−i
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iiiii−i−i−i−iii
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−iii−i−iii−i−i
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iii−i−iii
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−iiiii−i−i
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-1-111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-1-111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ33222-2-2222-2-2-2-222-2-22222-2-222-2-2-2-2-2-22222-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000002i−2i2i−2i00000000000000000000000000000000
χ34222-2-2222-2-2-2-222-2-22222-2-222-2-2-2-2-2-22222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ35222-2-2222-2-2-2-222-2-22222-2-222-2-2-2-2-2-222-2-222-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ36222-2-2222-2-2-2-222-2-22222-2-222-2-2-2-2-2-222-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000002i−2i2i−2i00000000000000000000000000000000
χ37222-2-2222-2-2-2-222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ38222-2-2222-2-2-2-222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ39222-2-2222-2-2-2-222-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ40222-2-2222-2-2-2-222-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ4122-22-22-2-222-2-22-22-22i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i−2i0000000000000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000002-22i−2i0000000000000000
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χ4322-22-22-2-222-2-22-22-22i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i−2i000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000-22−2i2i0000000000000000
χ4422-22-22-2-222-2-22-22-22i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i−2i000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000002-22i−2i0000000000000000
χ4522-22-22-2-222-2-22-22-2−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i0000000000000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000002-2−2i2i0000000000000000
χ4622-22-22-2-222-2-22-22-2−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i0000000000000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000-222i−2i0000000000000000
χ4722-22-22-2-222-2-22-22-2−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000-222i−2i0000000000000000
χ4822-22-22-2-222-2-22-22-2−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000002-2−2i2i0000000000000000
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χ5222-2-22-22-22-22-2-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000002i−2i2-20000000000000000000000000000
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χ5422-2-22-22-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000002i−2i-220000000000000000000000000000
χ5522-2-22-22-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000002i−2i-220000000000000000000000000000
χ5622-2-22-22-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000−2i2i2-20000000000000000000000000000
χ572-222-22-2-2-2-222-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ582-222-22-2-2-2-222-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ592-222-22-2-2-2-222-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ602-222-22-2-2-2-222-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-22-22−2i2i−2i2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ612-222-22-2-2-2-222-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ622-222-22-2-2-2-222-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ632-222-22-2-2-2-222-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ642-222-22-2-2-2-222-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-22-222i−2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ652-222-2-22-22-22-22-2-222i2i−2i−2i2i−2i−2i2i−2i−2i2i2i2i−2i−2i2i000000002i−2i2i−2i2-22-22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ662-222-2-22-22-22-22-2-222i2i−2i−2i2i−2i−2i2i−2i−2i2i2i2i−2i−2i2i000000002i−2i2i−2i2-22-2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ672-222-2-22-22-22-22-2-222i2i−2i−2i2i−2i−2i2i−2i−2i2i2i2i−2i−2i2i00000000−2i2i−2i2i-22-222ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ682-222-2-22-22-22-22-2-222i2i−2i−2i2i−2i−2i2i−2i−2i2i2i2i−2i−2i2i00000000−2i2i−2i2i-22-22−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.