Finite Group Databasebeta

← Group #8595

Character table — Group #8595

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order1222222244444444222244444444444444444444888888888888888888888888888888888888888888888888
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
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17111-1-11-1-1iiii−i−i−i−i11-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ18111-1-11-1-1iiii−i−i−i−i11-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ19111-1-11-1-1iiii−i−i−i−i11-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ20111-1-11-1-1iiii−i−i−i−i11-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ21111-1-11-1-1iiii−i−i−i−i-1-1111-1ii−i−i-1-111−i−i−i−iiiii1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ22111-1-11-1-1iiii−i−i−i−i-1-1111-1ii−i−i-1-111−i−i−i−iiiii1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ23111-1-11-1-1iiii−i−i−i−i-1-1111-1ii−i−i-1-111−i−i−i−iiiii1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−iζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ24111-1-11-1-1iiii−i−i−i−i-1-1111-1ii−i−i-1-111−i−i−i−iiiii1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ25111-1-11-1-1−i−i−i−iiiii11-1-11-1−i−iii11-1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ26111-1-11-1-1−i−i−i−iiiii11-1-11-1−i−iii11-1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ27111-1-11-1-1−i−i−i−iiiii11-1-11-1−i−iii11-1-1−i−i−i−iiiii1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ28111-1-11-1-1−i−i−i−iiiii11-1-11-1−i−iii11-1-1−i−i−i−iiiii1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ29111-1-11-1-1−i−i−i−iiiii-1-1111-1−i−iii-1-111iiii−i−i−i−i1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ30111-1-11-1-1−i−i−i−iiiii-1-1111-1−i−iii-1-111iiii−i−i−i−i1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ31111-1-11-1-1−i−i−i−iiiii-1-1111-1−i−iii-1-111iiii−i−i−i−i1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ32111-1-11-1-1−i−i−i−iiiii-1-1111-1−i−iii-1-111iiii−i−i−i−i1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
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χ342222222222222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000
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χ792-2-2222-2-2−2i2i2i−2i−2i2i2i−2i0000-222i−2i2i−2i0000000000002-22-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ802-2-2222-2-2−2i2i2i−2i−2i2i2i−2i0000-222i−2i2i−2i0000000000002-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ812-2-2-2-22222-2-22-222-20000222-2-22000000000000-2-200000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ822-2-2-2-22222-2-22-222-20000222-2-22000000000000-2-20000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ832-2-2-2-22222-2-22-222-20000-2-2-222-2000000000000222-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ842-2-2-2-22222-2-22-222-20000-2-2-222-200000000000022-222-22-2-222-2-22-222-200000000000000000000000000000000
χ852-2-2-2-2222-222-22-2-22000022-222-2000000000000-2-200000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ862-2-2-2-2222-222-22-2-22000022-222-2000000000000-2-20000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ872-2-2-2-2222-222-22-2-220000-2-22-2-22000000000000222-2-22-222-22-2-22-222-200000000000000000000000000000000
χ882-2-2-2-2222-222-22-2-220000-2-22-2-2200000000000022-222-22-2-22-222-22-2-2200000000000000000000000000000000

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