Finite Group Databasebeta

← Group #365421

Character table — Group #365421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444222222224444444444448888888888888888222244444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1
χ9111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ10111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ11111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ12111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ13111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ14111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ15111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1111111-1-1
χ16111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ171111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-11111-1-1-1-1ii−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i1-1i−i
χ181111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-11111-1-1-1-1ii−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-1111-1i−i11-1-1ii−i−iii−i−i−i−iii-1-111−i−iii-11−ii
χ191111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-11111-1-1-1-1ii−i−i-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i11-1-1-11−ii-1-111−i−iiiii−i−iii−i−i-1-111−i−iii-11−ii
χ201111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-11111-1-1-1-1ii−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111-11−ii-1-111−i−iiiii−i−i−i−iii11-1-1ii−i−i1-1i−i
χ211111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-1-1-1-1-11111ii−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1111-1i−i-1-111−i−iii−i−iii−i−iii11-1-1ii−i−i-11−ii
χ221111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-1-1-1-1-11111ii−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-11-1i−i-1-111−i−iii−i−iiiii−i−i-1-111−i−iii1-1i−i
χ231111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-1-1-1-1-11111ii−i−i-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i-1-111-11−ii11-1-1ii−i−i−i−iii−i−iii-1-111−i−iii1-1i−i
χ241111-1-1-1-111-1-111-1-111-1-1-1iiii−i−i−i−i11-1-1-1-1-11111ii−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1-11−ii11-1-1ii−i−i−i−iiiii−i−i11-1-1ii−i−i-11−ii
χ251111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-11111-1-1-1-1−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii1-1−ii
χ261111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-11111-1-1-1-1−i−iii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-1111-1−ii11-1-1−i−iii−i−iiiii−i−i-1-111ii−i−i-11i−i
χ271111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-11111-1-1-1-1−i−iii-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i−i−iii−i−iii-1-111ii−i−i-11i−i
χ281111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-11111-1-1-1-1−i−iii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111-11i−i-1-111ii−i−i−i−iiiii−i−i11-1-1−i−iii1-1−ii
χ291111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-1-1-1-1-11111−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1111-1−ii-1-111ii−i−iii−i−iii−i−i11-1-1−i−iii-11i−i
χ301111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-1-1-1-1-11111−i−iii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i11-1-11-1−ii-1-111ii−i−iii−i−i−i−iii-1-111ii−i−i1-1−ii
χ311111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-1-1-1-1-11111−i−iii-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii-1-111-11i−i11-1-1−i−iiiii−i−iii−i−i-1-111ii−i−i1-1−ii
χ321111-1-1-1-111-1-111-1-111-1-1-1−i−i−i−iiiii11-1-1-1-1-11111−i−iii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1-11i−i11-1-1−i−iiiii−i−i−i−iii11-1-1−i−iii-11i−i
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χ342222222222222222-2-2-2-2-222222222-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222222-2-2-2-200000000000000000000-2-2220000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-222220000000000000000000022-2-20000000000000000000000000000
χ372222-2-2-2-222-2-222-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2-2200000000−2i−2i2i2i22-2-22i2i−2i−2i00000000000000000000-22−2i2i0000000000000000000000000000
χ382222-2-2-2-222-2-222-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2-2200000000−2i−2i2i2i-2-222−2i−2i2i2i000000000000000000002-22i−2i0000000000000000000000000000
χ392222-2-2-2-222-2-222-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-22000000002i2i−2i−2i22-2-2−2i−2i2i2i00000000000000000000-222i−2i0000000000000000000000000000
χ402222-2-2-2-222-2-222-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-22000000002i2i−2i−2i-2-2222i2i−2i−2i000000000000000000002-2−2i2i0000000000000000000000000000
χ41222-222222-2-2-2-2-2-2-22-222-2000000002-2-222-2-222-2-200000000000022-2-222-2-2000000002-22-200000000000000000000000000000000
χ42222-222222-2-2-2-2-2-2-22-222-2000000002-2-222-2-222-2-2000000000000-2-222-2-22200000000-22-2200000000000000000000000000000000
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χ47222-2-2-2-2-22-222-2-2222-2-2-22000000002-22-2-22222-2-200000000000022-2-2-2-22200000000-222-200000000000000000000000000000000
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χ5322-2-222-2-2-2-22222-2-200000−2i−2i2i2i−2i−2i2i2i0000000000000002-22-2−2i2i−2i2i2−22−22−22−2−i2−i2i2i2−i2−i2i2i20000000000000000000000002−22−2−i2i2−i2i20000
χ5422-2-222-2-2-2-22222-2-200000−2i−2i2i2i−2i−2i2i2i0000000000000002-22-2−2i2i−2i2i−22−22−22−22i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−22i2−i2i2−i20000
χ5522-2-222-2-2-2-22222-2-200000−2i−2i2i2i−2i−2i2i2i000000000000000-22-222i−2i2i−2i2−22−22−22−2−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−22i2−i2i2−i20000
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χ5822-2-2-2-222-2-2-2-222220000022-2-2-2-2220000000000000002-2-222-2-22−22−222−22−2−2−22222−2−2000000000000000000000000−222−2−222−20000
χ5922-2-2-2-222-2-2-2-222220000022-2-2-2-222000000000000000-222-2-222-22−22−2−22−2222−2−2−2−222000000000000000000000000−222−2−222−20000
χ6022-2-2-2-222-2-2-2-222220000022-2-2-2-222000000000000000-222-2-222-2−22−222−22−2−2−22222−2−20000000000000000000000002−2−222−2−220000
χ6122-2-2-2-222-2-2-2-2222200000-2-22222-2-20000000000000002-2-22-222-22−22−2−22−22−2−22222−2−20000000000000000000000002−2−22−222−20000
χ6222-2-2-2-222-2-2-2-2222200000-2-22222-2-20000000000000002-2-22-222-2−22−222−22−222−2−2−2−222000000000000000000000000−222−22−2−220000
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χ6422-2-2-2-222-2-2-2-2222200000-2-22222-2-2000000000000000-222-22-2-22−22−222−22−222−2−2−2−2220000000000000000000000002−2−22−222−20000
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χ954-4444-4-44-4-4-44-444-4000000000000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ964-4444-4-44-4-4-44-444-400000000000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ974-444-444-4-4-44-4-44-440000000000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ984-444-444-4-4-44-4-44-4400000000000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ994-44-44-4-44-444-44-4-44000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-4-44-444-44-4-4400000-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4-444-4-44-444-44-4000004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-444-4-44-444-44-400000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-44-44-444-44-44-444-44-4400000000-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-44-44444-4-444-44-4-44-400000000-444000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).