Finite Group Databasebeta

← Group #10692225

Character table — Group #10692225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444444488888888888888888816161616161616161616242424242424242448484848
order12222236662244446666661212121244444444121212121212121212122466121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-111111-11-11-111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i1-111-1-1ii−i−i1-11-1i−ii−ii−i1-1
χ101111-1-111111-11-11-111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i1-111-1-1ii−i−i-11-11−ii−ii−ii-11
χ111111-1-111111-11-11-111-1-1-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-11-1-111ii−i−i1-11-1i−ii−i−ii-11
χ121111-1-111111-11-11-111-1-1-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-11-1-111ii−i−i-11-11−ii−iii−i1-1
χ131111-1-111111-11-11-111-1-1-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-11-1-111−i−iii1-11-1−ii−iii−i-11
χ141111-1-111111-11-11-111-1-1-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-11-1-111−i−iii-11-11i−ii−i−ii1-1
χ151111-1-111111-11-11-111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii1-111-1-1−i−iii1-11-1−ii−ii−ii1-1
χ161111-1-111111-11-11-111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii1-111-1-1−i−iii-11-11i−ii−ii−i-11
χ17222222222222-2-2-2-2222222-2-2-2-22-22-20000-2-2000000000000002-22-2000000000000
χ18222222222222-2-2-2-2222222-2-2-2-2-22-220000-2-200000000000000-22-22000000000000
χ192222222222-2-22-2-22-2-22-2-2222-2-200000000-22000000000000000000000022-2-20000
χ202222222222-2-22-2-22-2-22-2-2222-2-200000000-220000000000000000000000-2-2220000
χ212222222222-2-2-222-2-2-22-2-22-2-222000000002-200000000000000000022-2-200000000
χ222222222222-2-2-222-2-2-22-2-22-2-222000000002-2000000000000000000-2-22200000000
χ23222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ24222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-2-21111-1-1-1-1000000000000
χ25222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ26222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111122-1-1-1-11111000000000000
χ27222222-1-1-1-122-2-2-2-2-1-1-1-1-1-111112-22-2000011−i3−i3i3i3−i3−i3i3i300−i3i3−i3i3-11-11000000000000
χ28222222-1-1-1-122-2-2-2-2-1-1-1-1-1-111112-22-2000011i3i3−i3−i3i3i3−i3−i300i3−i3i3−i3-11-11000000000000
χ29222222-1-1-1-122-2-2-2-2-1-1-1-1-1-11111-22-22000011−i3−i3i3i3−i3−i3i3i300i3−i3i3−i31-11-1000000000000
χ30222222-1-1-1-122-2-2-2-2-1-1-1-1-1-11111-22-22000011i3i3−i3−i3i3i3−i3−i300−i3i3−i3i31-11-1000000000000
χ312222-2-222222-2-22-2222-2-2-2-2-2-2222i−2i−2i2i0000-22000000000000002i−2i−2i2i000000000000
χ322222-2-222222-2-22-2222-2-2-2-2-2-222−2i2i2i−2i0000-2200000000000000−2i2i2i−2i000000000000
χ332222-2-22222-2222-2-2-2-2-222-2222200000000-2-200000000000000000000002i−2i−2i2i0000
χ342222-2-22222-2222-2-2-2-2-222-2222200000000-2-20000000000000000000000−2i2i2i−2i0000
χ352222-2-22222-22-2-222-2-2-222-2-2-2-2-200000000220000000000000000002-2-2200000000
χ362222-2-22222-22-2-222-2-2-222-2-2-2-2-20000000022000000000000000000-222-200000000
χ372222-2-2-1-1-1-12-22-22-2-1-11111-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii2-2-1-111−i−iii000000000000
χ382222-2-2-1-1-1-12-22-22-2-1-11111-1-1112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i-2211-1-1−i−iii000000000000
χ392222-2-2-1-1-1-12-22-22-2-1-11111-1-111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii-2211-1-1ii−i−i000000000000
χ402222-2-2-1-1-1-12-22-22-2-1-11111-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i2-2-1-111ii−i−i000000000000
χ412222-2-2-1-1-1-12-2-22-22-1-1111111-1-12i−2i−2i2i00001-133−3−3−3−33300−i3i3i3−i3−iii−i000000000000
χ422222-2-2-1-1-1-12-2-22-22-1-1111111-1-12i−2i−2i2i00001-1−3−33333−3−300i3−i3−i3i3−iii−i000000000000
χ432222-2-2-1-1-1-12-2-22-22-1-1111111-1-1−2i2i2i−2i00001-133−3−3−3−33300i3−i3−i3i3i−i−ii000000000000
χ442222-2-2-1-1-1-12-2-22-22-1-1111111-1-1−2i2i2i−2i00001-1−3−33333−3−300−i3i3i3−i3i−i−ii000000000000
χ45444444-2-2-2-2-4-44-4-4422-222-2-2-222000000002-2000000000000000000000000000000
χ46444444-2-2-2-2-4-4-444-422-222-222-2-200000000-22000000000000000000000000000000
χ474444-4-4-2-2-2-2-4444-4-4222-2-22-2-2-2-20000000022000000000000000000000000000000
χ484444-4-4-2-2-2-2-44-4-444222-2-22222200000000-2-2000000000000000000000000000000
χ4944-4-44-44-44-400000000400-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ5044-4-44-44-44-400000000400-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ5144-4-44-4-22-22000000−2i32i3-2−2i32i32000000002i−2i2i−2i002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ5244-4-44-4-22-22000000−2i32i3-2−2i32i3200000000−2i2i−2i2i00−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ5344-4-44-4-22-220000002i3−2i3-22i3−2i32000000002i−2i2i−2i002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ5444-4-44-4-22-220000002i3−2i3-22i3−2i3200000000−2i2i−2i2i00−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ5544-4-4-444-44-400000000-4004000000002-2-22002-22-2-22-220000000000000000000000
χ5644-4-4-444-44-400000000-400400000000-222-200-22-222-22-20000000000000000000000
χ5744-4-4-44-22-22000000−2i32i322i3−2i3-2000000002-2-2200−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ5844-4-4-44-22-22000000−2i32i322i3−2i3-200000000-222-2001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000
χ5944-4-4-44-22-220000002i3−2i32−2i32i3-2000000002-2-2200−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ6044-4-4-44-22-220000002i3−2i32−2i32i3-200000000-222-2001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000
χ618-88-8008-8-8800000000000000000000000000000000000000000000000000000000
χ628-88-800-444-4000000000000−4i34i3000000000000000000000000000000000000000000
χ638-88-800-444-40000000000004i3−4i3000000000000000000000000000000000000000000
χ648-8-880088-8-800000000000000000000000000000000000000000000000000000000
χ658-8-8800-4-4440000000000000043−430000000000000000000000000000000000000000
χ668-8-8800-4-44400000000000000−43430000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.