Finite Group Databasebeta

← Group #8784

Character table — Group #8784

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order1222222244444444444444444444444444444444888888888888888888888888888888888888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171111-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ181111-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ191111-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ201111-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ211111-1-1-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ221111-1-1-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ231111-1-1-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−iζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ241111-1-1-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ251111-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ261111-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ271111-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ281111-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ291111-1-1-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ301111-1-1-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ311111-1-1-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ321111-1-1-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ332222222222222222-2-2-2-222-2-222-2-222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-222-2-222-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-22222-2-222-2-22222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
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χ382222-2-2-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000
χ392222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i22-2-2-2-222−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000
χ402222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2-22222-2-22i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000
χ4122-2-222-2-22222-2-2-2-20000002-2002-2002-2002-2000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ4222-2-222-2-22222-2-2-2-20000002-2002-2002-2002-20000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ4322-2-222-2-22222-2-2-2-2000000-2200-2200-2200-22000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ4422-2-222-2-22222-2-2-2-2000000-2200-2200-2200-220000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ4522-2-222-2-2-2-2-2-222220000002-2002-200-2200-22000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4622-2-222-2-2-2-2-2-222220000002-2002-200-2200-220000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4722-2-222-2-2-2-2-2-22222000000-2200-22002-2002-2000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4822-2-222-2-2-2-2-2-22222000000-2200-22002-2002-20000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
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χ842-2-22-222-22i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000-222-2−2i2i2i−2i2i−2i−2i2i2-2-22-222-200000000000000000000000000000000
χ852-2-22-222-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000-222-22i−2i−2i2i−2i2i2i−2i2-2-22-222-200000000000000000000000000000000
χ862-2-22-222-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000-222-2−2i2i2i−2i2i−2i−2i2i-222-22-2-2200000000000000000000000000000000
χ872-2-22-222-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000002-2-2200000000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-20000000000000000
χ882-2-22-222-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000002-2-220000000000000000−2i2i2i−2i2i−2i−2i2i-222-22-2-220000000000000000

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