Finite Group Databasebeta

← Group #382515

Character table — Group #382515

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111111111111111111111444444444444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444222244444444444444444444222244444444444488888888888888888888888888888888
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ201111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ211111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ231111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ241111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
χ332222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-2000000000000000022-2-22-22-2000000002-22-200000000000000000000000000000000
χ342222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-2000000000000000022-2-2-22-2200000000-22-2200000000000000000000000000000000
χ352222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2220000000000000000-2-2222-2-22000000002-2-2200000000000000000000000000000000
χ362222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2220000000000000000-2-222-222-200000000-222-200000000000000000000000000000000
χ372222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-22222222222-2-20000000000000000-2-2222-2-2200000000-222-200000000000000000000000000000000
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χ392222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222222222-2-222000000000000000022-2-22-22-200000000-22-2200000000000000000000000000000000
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χ422222-2-2-222-2-222-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000022-2-22i2i−2i−2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000
χ432222-2-2-222-2-222-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000-2-222−2i−2i2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000
χ442222-2-2-222-2-222-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000-2-222−2i−2i2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000
χ452222-2-2-222-2-222-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000022-2-2−2i−2i2i2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000
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χ482222-2-2-222-2-222-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000-2-2222i2i−2i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000
χ4922-2-222-22-22-22-22-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000022-2-22i2i−2i−2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ30000000000000000
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χ5422-2-222-22-22-22-22-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000022-2-2−2i−2i2i2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ5522-2-222-22-22-22-22-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000-2-2222i2i−2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ5622-2-222-22-22-22-22-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000-2-2222i2i−2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
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χ842-2-22-222-2-22222-2-2-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000-222-2−2i2i2i−2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000002ζ−2ζ2ζ3−2ζ3
χ852-2-22-222-2-22222-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000002-2-22−2i2i2i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000002ζ3−2ζ32ζ−2ζ
χ862-2-22-222-2-22222-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000002-2-22−2i2i2i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000−2ζ32ζ3−2ζ2ζ
χ872-2-22-222-2-22222-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000-222-22i−2i−2i2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000−2ζ32ζ3−2ζ2ζ
χ882-2-22-222-2-22222-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000-222-22i−2i−2i2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000002ζ3−2ζ32ζ−2ζ
χ894444-4-4-4-4-444-4-444-44i4i4i4i−4i−4i−4i−4i−4i−4i−4i−4i4i4i4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ904444-4-4-4-4-444-4-444-4−4i−4i−4i−4i4i4i4i4i4i4i4i4i−4i−4i−4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-4-44-44-44-44-44i4i−4i−4i4i4i−4i−4i−4i−4i4i4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-444-4-44-44-44-44-4−4i−4i4i4i−4i−4i4i4i4i4i−4i−4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-4-444-4-444-4-44444-4-4-4-44444-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-4-4-444-4-444-4-444-4-44444-4-4-4-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-4-4-44-444-4-444-4444-4-4-4-444-4-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-4-44-444-4-444-44-4-44444-4-444-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ974-44-44-444-44-4-44-44-44i−4i4i−4i4i−4i4i−4i−4i4i−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44-44-444-44-4-44-44-4−4i4i−4i4i−4i4i−4i4i4i−4i4i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ994-44-4-44-44-4-44-444-444-44-4-44-44-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-44-44-4-44-444-44-44-444-44-44-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4-44-4-444-44-4-4444-44-4-44-444-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-44-4-444-44-4-444-44-444-44-4-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-44444-4-4-4-444-44i−4i−4i4i−4i4i4i−4i−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-44444-4-4-4-444-4−4i4i4i−4i4i−4i−4i4i4i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.