Finite Group Databasebeta

← Group #368778

Character table — Group #368778

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12224444222222222244444444444444444422444444444444442244444444444444444444448888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ911111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1
χ1011111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-111-1-1-111
χ1111111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111
χ1211111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-1
χ1311111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1
χ1411111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-111
χ1511111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-111
χ1611111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-111-1-1
χ171111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1iiii−i−i−i−i11-11-1ii−i−iiiii−i−i−i−i1-111-1-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-1i−ii−i
χ181111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1iiii−i−i−i−i11-11-1ii−i−iiiii−i−i−i−i1-111-1-11-1ii−i−i−i−iii−i−iiiii−i−i-1-111-1-111-1-111−ii−ii
χ191111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1iiii−i−i−i−i11-11-1ii−i−iiiii−i−i−i−i-11-1-111-11−i−iiiii−i−iii−i−i−i−iii11-1-111-1-1-1-111−ii−ii
χ201111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1iiii−i−i−i−i11-11-1ii−i−iiiii−i−i−i−i-11-1-111-11−i−iii−i−iii−i−iii−i−iii-1-111-1-11111-1-1i−ii−i
χ211111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1−i−i−i−iiiii11-11-1−i−iii−i−i−i−iiiii1-111-1-11-1−i−iiiii−i−iii−i−i−i−iii-1-111-1-111-1-111i−ii−i
χ221111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1−i−i−i−iiiii11-11-1−i−iii−i−i−i−iiiii1-111-1-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-1−ii−ii
χ231111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1−i−i−i−iiiii11-11-1−i−iii−i−i−i−iiiii-11-1-111-11ii−i−iii−i−iii−i−iii−i−i-1-111-1-11111-1-1−ii−ii
χ241111-1-1-1-111-111-1-1-1-1-1111-1-111-1-1−i−i−i−iiiii11-11-1−i−iii−i−i−i−iiiii-11-1-111-11ii−i−i−i−iii−i−iiiii−i−i11-1-111-1-1-1-111i−ii−i
χ251111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111iiii−i−i−i−i1-11-11ii−i−i−i−i−i−iiiii1-1-1-1111-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-1111-11-1i−i−ii
χ261111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111iiii−i−i−i−i1-11-11ii−i−i−i−i−i−iiiii1-1-1-1111-1−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1-11-11−iii−i
χ271111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111iiii−i−i−i−i1-11-11ii−i−i−i−i−i−iiiii-1111-1-1-11ii−i−iii−i−i−i−iii−i−iii11-1-1-1-111-11-11−iii−i
χ281111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111iiii−i−i−i−i1-11-11ii−i−i−i−i−i−iiiii-1111-1-1-11ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-11-11-1i−i−ii
χ291111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111−i−i−i−iiiii1-11-11−i−iiiiiii−i−i−i−i1-1-1-1111-1ii−i−iii−i−i−i−iii−i−iii-1-11111-1-1-11-11i−i−ii
χ301111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111−i−i−i−iiiii1-11-11−i−iiiiiii−i−i−i−i1-1-1-1111-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-1111-11-1−iii−i
χ311111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111−i−i−i−iiiii1-11-11−i−iiiiiii−i−i−i−i-1111-1-1-11−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-11-11-1−iii−i
χ321111-1-1-1-111-1-1-111-1-1-1111-1-1-1-111−i−i−i−iiiii1-11-11−i−iiiiiii−i−i−i−i-1111-1-1-11−i−iii−i−iiiii−i−iii−i−i11-1-1-1-111-11-11i−i−ii
χ332222222222-222-2-2-2-2-2-2-2-222-2-22200000000-22-2-22000000000000000000002i−2i2i−2i000000002i−2i2i−2i0000000000000000
χ342222222222-222-2-2-2-2-2-2-2-222-2-22200000000-22-2-2200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000000000
χ352222222222-2-2-222-2-2-2-2-2-22222-2-200000000-2-222-2000000000000000000002i−2i2i−2i00000000−2i2i−2i2i0000000000000000
χ362222222222-2-2-222-2-2-2-2-2-22222-2-200000000-2-222-200000000000000000000−2i2i−2i2i000000002i−2i2i−2i0000000000000000
χ3722222222-2-222222-22-22-2-2-2-22222000000002-2-2-2-20000000000002-22-22-2-2200000000000000000000000000000000
χ3822222222-2-222222-22-22-2-2-2-22222000000002-2-2-2-2000000000000-22-22-222-200000000000000000000000000000000
χ3922222222-2-22-2-2-2-2-22-22-2-2-2-2-2-2-2-200000000222220000000000002-2-22-22-2200000000000000000000000000000000
χ4022222222-2-22-2-2-2-2-22-22-2-2-2-2-2-2-2-20000000022222000000000000-222-22-22-200000000000000000000000000000000
χ4122222222-2-2-222-2-22-22-222-2-2-2-22222222222-2-222-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ4222222222-2-2-222-2-22-22-222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-22222-2-222-2-2220000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2222-22-222-2-222-2-222222222-22-2-22-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2222-22-222-2-222-2-2-2-2-2-2-2-2-2-2-22-2-22222222-2-222-2-20000000000000000000000000000000000000000
χ452222-2-2-2-22222222222-2-2-2-2-2-2-2-2-200000000-222-2-2000000000000000000002-2-22000000002-2-220000000000000000
χ462222-2-2-2-22222222222-2-2-2-2-2-2-2-2-200000000-222-2-200000000000000000000-222-200000000-222-20000000000000000
χ472222-2-2-2-2222-2-2-2-2222-2-2-2-2-2222200000000-2-2-222000000000000000000002-2-2200000000-222-20000000000000000
χ482222-2-2-2-2222-2-2-2-2222-2-2-2-2-2222200000000-2-2-22200000000000000000000-222-2000000002-2-220000000000000000
χ492222-2-2-2-2-2-222222-22-2-22222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ502222-2-2-2-2-2-222222-22-2-22222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ512222-2-2-2-2-2-22-2-2-2-2-22-2-2222222222i2i2i2i−2i−2i−2i−2i-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ522222-2-2-2-2-2-22-2-2-2-2-22-2-222222222−2i−2i−2i−2i2i2i2i2i-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-222-2-22-222-2-22222-2-2000000002-22-22000000000000222-2-22-2-200000000000000000000000000000000
χ542222-2-2-2-2-2-2-222-2-22-222-2-22222-2-2000000002-22-22000000000000-2-2-222-22200000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2-2222-222-2-222-2-2220000000022-22-200000000000022-222-2-2-200000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2222-222-2-222-2-2220000000022-22-2000000000000-2-22-2-222200000000000000000000000000000000
χ572-2-2222-2-22-2200002-2-2-22-22-200002i2i−2i−2i2i2i−2i−2i200002i−2i2i−2i000000000000000000002i−2i2i−2i000000002-22-2000000000000
χ582-2-2222-2-22-2200002-2-2-22-22-200002i2i−2i−2i2i2i−2i−2i200002i−2i2i−2i00000000000000000000−2i2i−2i2i00000000-22-22000000000000
χ592-2-2222-2-22-2200002-2-2-22-22-20000−2i−2i2i2i−2i−2i2i2i20000−2i2i−2i2i000000000000000000002i−2i2i−2i00000000-22-22000000000000
χ602-2-2222-2-22-2200002-2-2-22-22-20000−2i−2i2i2i−2i−2i2i2i20000−2i2i−2i2i00000000000000000000−2i2i−2i2i000000002-22-2000000000000
χ612-2-2222-2-2-22-2000022-222-2-2200002i2i−2i−2i2i2i−2i−2i-20000−2i2i−2i2i0000000000000000000000002-22-2000000002i−2i2i−2i00000000
χ622-2-2222-2-2-22-2000022-222-2-2200002i2i−2i−2i2i2i−2i−2i-20000−2i2i−2i2i000000000000000000000000-22-2200000000−2i2i−2i2i00000000
χ632-2-2222-2-2-22-2000022-222-2-220000−2i−2i2i2i−2i−2i2i2i-200002i−2i2i−2i0000000000000000000000002-22-200000000−2i2i−2i2i00000000
χ642-2-2222-2-2-22-2000022-222-2-220000−2i−2i2i2i−2i−2i2i2i-200002i−2i2i−2i000000000000000000000000-22-22000000002i−2i2i−2i00000000
χ652-2-22-2-2222-2-20000-222-22-2-22000022-2-2-2-222200002-2-22000000000000000000002-2-22000000002-2-22000000000000
χ662-2-22-2-2222-2-20000-222-22-2-22000022-2-2-2-222200002-2-2200000000000000000000-222-200000000-222-2000000000000
χ672-2-22-2-2222-2-20000-222-22-2-220000-2-22222-2-220000-222-2000000000000000000002-2-2200000000-222-2000000000000
χ682-2-22-2-2222-2-20000-222-22-2-220000-2-22222-2-220000-222-200000000000000000000-222-2000000002-2-22000000000000
χ692-2-22-2-222-2220000-2-2222-22-2000022-2-2-2-222-20000-222-20000000000000000000000002i−2i−2i2i00000000−2i2i2i−2i00000000
χ702-2-22-2-222-2220000-2-2222-22-2000022-2-2-2-222-20000-222-2000000000000000000000000−2i2i2i−2i000000002i−2i−2i2i00000000
χ712-2-22-2-222-2220000-2-2222-22-20000-2-22222-2-2-200002-2-220000000000000000000000002i−2i−2i2i000000002i−2i−2i2i00000000
χ722-2-22-2-222-2220000-2-2222-22-20000-2-22222-2-2-200002-2-22000000000000000000000000−2i2i2i−2i00000000−2i2i2i−2i00000000
χ7344-4-44i−4i4i−4i000004-4000000004i−4i002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000002−2i−2+2i002+2i−2−2i0000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i000004-4000000004i−4i00−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000−2+2i2−2i00−2−2i2+2i0000000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i00000-4400000000−4i4i002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000−2+2i2−2i00−2−2i2+2i0000000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i00000-4400000000−4i4i00−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000002−2i−2+2i002+2i−2−2i0000000000000000000000000000000000000000
χ7744-4-4−4i4i−4i4i000004-400000000−4i4i002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000002+2i−2−2i002−2i−2+2i0000000000000000000000000000000000000000
χ7844-4-4−4i4i−4i4i000004-400000000−4i4i00−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000−2−2i2+2i00−2+2i2−2i0000000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i00000-44000000004i−4i002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000−2−2i2+2i00−2+2i2−2i0000000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i00000-44000000004i−4i00−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000000000002+2i−2−2i002−2i−2+2i0000000000000000000000000000000000000000
χ814-44-44i−4i−4i4i0004-40000000000004i−4i2−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000002−2i−2+2i002+2i−2−2i000000000000000000000000000000000000000000
χ824-44-44i−4i−4i4i0004-40000000000004i−4i−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000000000000000000000
χ834-44-44i−4i−4i4i000-44000000000000−4i4i2−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000000000000000000000
χ844-44-44i−4i−4i4i000-44000000000000−4i4i−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000002−2i−2+2i002+2i−2−2i000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i0004-4000000000000−4i4i2+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000002+2i−2−2i002−2i−2+2i000000000000000000000000000000000000000000
χ864-44-4−4i4i4i−4i0004-4000000000000−4i4i−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000000000000000000000
χ874-44-4−4i4i4i−4i000-440000000000004i−4i2+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i000-440000000000004i−4i−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000002+2i−2−2i002−2i−2+2i000000000000000000000000000000000000000000
χ894-4-4444-4-44-4-40000-4444-444-4000000000000-400000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-4440000-4-44-4-44-44000000000000400000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-4400004-4-44-44-44000000000000-400000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-4000044-4-4-444-4000000000000400000000000000000000000000000000000000000000000000000000

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