Finite Group Databasebeta

← Group #375840

Character table — Group #375840

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444444448888888888888888222222224444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ171111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-11-1ii−i−i11-1-1i−iii−i−iii−i−i11-1-11-1i−i
χ181111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-111-1-11-1ii−i−i-1-111i−i−i−iii−i−iii-1-111-11−ii
χ191111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111-1-1111-1−i−iii-1-111i−i−i−iiiii−i−i11-1-1-11−ii
χ201111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111-1-1111-1−i−iii11-1-1i−iii−i−i−i−iii-1-1111-1i−i
χ211111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1-1-111-11−i−iii11-1-1−iiii−i−i−i−iii-1-111-11−ii
χ221111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1-1-111-11−i−iii-1-111−ii−i−iiiii−i−i11-1-11-1i−i
χ231111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-11111-1-1-11ii−i−i-1-111−ii−i−iii−i−iii-1-1111-1i−i
χ241111-1-1-1-1111-1-11-1-111-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-11111-1-1-11ii−i−i11-1-1−iiii−i−iii−i−i11-1-1-11−ii
χ251111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111-1-1111-1ii−i−i11-1-1−ii−i−iiiii−i−i-1-1111-1−ii
χ261111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111-1-1111-1ii−i−i-1-111−iiii−i−i−i−iii11-1-1-11i−i
χ271111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-111-1-11-1−i−iii-1-111−iiii−i−iii−i−i-1-111-11i−i
χ281111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-11-1−i−iii11-1-1−ii−i−iii−i−iii11-1-11-1−ii
χ291111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-11111-1-1-11−i−iii11-1-1i−i−i−iii−i−iii11-1-1-11i−i
χ301111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-11111-1-1-11−i−iii-1-111i−iii−i−iii−i−i-1-1111-1−ii
χ311111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1-1-111-11ii−i−i-1-111i−iii−i−i−i−iii11-1-11-1−ii
χ321111-1-1-1-1111-1-11-1-111-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1-1-111-11ii−i−i11-1-1i−i−i−iiiii−i−i-1-111-11i−i
χ332222222222222222-2-2-2-222222222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000-2-200000000-2-20000000000000000
χ342222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002200000000220000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-200000000220000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000002200000000-2-20000000000000000
χ372222-2-2-2-2222-2-22-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000-2200000000−2i2i0000000000000000
χ382222-2-2-2-2222-2-22-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000002-2000000002i−2i0000000000000000
χ392222-2-2-2-2222-2-22-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000-22000000002i−2i0000000000000000
χ402222-2-2-2-2222-2-22-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000002-200000000−2i2i0000000000000000
χ41222-2222-2-2-2-22-22-2-2-2-22-200000000222-20000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000002-22-2000000000000000000
χ42222-2222-2-2-2-22-22-2-2-2-22-200000000222-20000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000-22-22000000000000000000
χ43222-2222-2-2-2-22-22-2-2-2-22-200000000222-2000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000-22-22000000000000000000
χ44222-2222-2-2-2-22-22-2-2-2-22-200000000222-2000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000002-22-2000000000000000000
χ45222-2-2-2-22-2-2-2-22222-2-2-220000000022-2200000000000022-2-2-2-22222-2-2-2-22200000000000000000000002-2-22000000000000000000
χ46222-2-2-2-22-2-2-2-22222-2-2-220000000022-2200000000000022-2-2-2-222-2-22222-2-20000000000000000000000-222-2000000000000000000
χ47222-2-2-2-22-2-2-2-22222-2-2-220000000022-22000000000000-2-22222-2-222-2-2-2-2220000000000000000000000-222-2000000000000000000
χ48222-2-2-2-22-2-2-2-22222-2-2-220000000022-22000000000000-2-22222-2-2-2-22222-2-200000000000000000000002-2-22000000000000000000
χ4922-2222-2-22-2-2-22-22-200002i2i−2i−2i2i2i−2i−2i00002-22-200002i−2i2i−2i000000002−22−22−22−2i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−2i2−i2i2−i20000
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χ5122-2222-2-22-2-2-22-22-200002i2i−2i−2i2i2i−2i−2i0000-22-220000−2i2i−2i2i000000002−22−22−22−2i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−22−i2i2−i2i20000
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χ5422-2222-2-22-2-2-22-22-20000−2i−2i2i2i−2i−2i2i2i00002-22-20000−2i2i−2i2i00000000−22−22−22−22i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−22i2−i2i2−i20000
χ5522-2222-2-22-2-2-22-22-20000−2i−2i2i2i−2i−2i2i2i0000-22-2200002i−2i2i−2i000000002−22−22−22−2−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−22i2−i2i2−i20000
χ5622-2222-2-22-2-2-22-22-20000−2i−2i2i2i−2i−2i2i2i0000-22-2200002i−2i2i−2i00000000−22−22−22−22i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−2−i2i2−i2i20000
χ5722-22-2-2222-2-22-2-2-22000022-2-2-2-22200002-2-2200002-2-2200000000i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ5822-22-2-2222-2-22-2-2-22000022-2-2-2-22200002-2-2200002-2-2200000000−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ5922-22-2-2222-2-22-2-2-22000022-2-2-2-2220000-222-20000-222-200000000i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
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χ6122-22-2-2222-2-22-2-2-220000-2-22222-2-200002-2-220000-222-200000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ6222-22-2-2222-2-22-2-2-220000-2-22222-2-200002-2-220000-222-200000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ6322-22-2-2222-2-22-2-2-220000-2-22222-2-20000-222-200002-2-2200000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ6422-22-2-2222-2-22-2-2-220000-2-22222-2-20000-222-200002-2-2200000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ652-2-222-22-2-2-22-2-22222-2-2-2000000002-2220000000000002-22-22-22-2000000002-22-22-22-2000000000000000000002-22-2000000000000
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χ672-2-222-22-2-2-22-2-22222-2-2-2000000002-222000000000000-22-22-22-22000000002-22-22-22-200000000000000000000-22-22000000000000
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χ722-2-22-22-22-2-22222-2-22-222000000002-2-2-2000000000000−2i2i−2i2i2i−2i2i−2i00000000-22-222-22-2000000000000000000002i−2i−2i2i000000000000
χ732-2-2-22-22222-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i-22-2200002i−2i2i−2i000000000000000000000000000000002-22-2002i−2i2i−2i0000000000000000000000
χ742-2-2-22-22222-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i-22-2200002i−2i2i−2i00000000000000000000000000000000-22-2200−2i2i−2i2i0000000000000000000000
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χ862-2-2-2-22-2-222-22-2222-222-22-22-2-22-222-2-220000-222-20000-222-22-2-220000000000000000-222-200000000000000000000000000000000
χ872-2-2-2-22-2-222-22-2222-222-2-22-222-22-22-2-2200002-2-2200002-2-22-222-20000000000000000-222-200000000000000000000000000000000
χ882-2-2-2-22-2-222-22-2222-222-2-22-222-22-22-2-2200002-2-220000-222-22-2-2200000000000000002-2-2200000000000000000000000000000000
χ89444-4444-4-4-4-44-44-4-444-4400000000-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-4-44-4-4-4-44444444-400000000-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-44-444-4-4-4-440000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ9244-4-444-44-444-4-4-4-44000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ9344-4-4-4-44-4-44444-44-400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ9444-4-4-4-44-4-44444-44-4000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ954-4444-4-44-44-44-4-44-4000000000000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ964-4444-4-44-44-44-4-44-400000000000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ974-444-444-4-44-4-44-4-44000000000000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ984-444-444-4-44-4-44-4-4400000000000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ994-44-44-4-4-44-4444-4-4400004-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-4-4-44-4444-4-440000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4-44444-44-4-4-44-400004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-44444-44-4-4-44-40000−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-444-44-4-4-44-4-4444-444400000000-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-44-44-4-44444-4-4-44-4-400000000-4444000000000000000000000000000000000000000000000000000000000000000000000000

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