Finite Group Databasebeta

← Group #108586

Character table — Group #108586

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444224444444444444444448888888888888888224488888888888888888888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11-11-1i−ii−ii−ii−i1-11-1
χ181111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-11-11−ii−ii−ii−ii-11-11
χ191111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-11-1i−ii−i−ii−ii-11-11
χ201111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-11-11−ii−iii−ii−i1-11-1
χ211111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-11-1−ii−iii−ii−i-11-11
χ221111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-11-11i−ii−i−ii−ii1-11-1
χ231111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11-11-1−ii−ii−ii−ii1-11-1
χ241111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-11-11i−ii−ii−ii−i-11-11
χ251111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−ii-111-1-111-1i−i−ii
χ261111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i1-1-111-1-11−iii−i
χ271111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−ii-111-11-1-11−iii−i
χ281111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−i1-1-11-111-1i−i−ii
χ291111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii1-1-11-111-1−iii−i
χ301111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−i-111-11-1-11i−i−ii
χ311111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−ii1-1-111-1-11i−i−ii
χ321111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i-111-1-111-1−iii−i
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χ342222222222-2-222-2-2-2-2-2-2222222220000000000000000-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ352222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ362222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ3722222222-2-222-2-222-2-2-2-222-2-222-2-200000000000000002-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822222222-2-222-2-222-2-2-2-222-2-222-2-200000000000000002-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922222222-2-222-2-222-2-2-2-2-2-222-2-2220000000000000000-22-220000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4022222222-2-222-2-222-2-2-2-2-2-222-2-2220000000000000000-22-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4122222222-2-2-2-2-2-2-2-2222222-2-222-2-22222-2-2-2-22222-2-2-2-2-22-22000000000000000022-2-222-2-200000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-2-22222-2-2-2-22222-22-220000000000000000-2-222-2-22200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-222-2-2222222-2-2-2-22222-2-2-2-22-22-20000000000000000-2-222-2-22200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-22222-2-2-2-222222-22-2000000000000000022-2-222-2-200000000000000000000000000000000
χ452222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-20000000000000000-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ462222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-20000000000000000-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-222-2-222-2-2-2-22222000000000000000022-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ482222-2-2-2-222-2-2-2-222-2-222-2-2-2-22222000000000000000022-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ492222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22200000000000000002-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
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χ542222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
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χ562222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2-2-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.