Finite Group Databasebeta

← Group #10692209

Character table — Group #10692209

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222444444444444444488888888888888888816161616161616161616242424242424242448484848
order12222236662244446666121212121212444444446121212121212121212881212121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ91111-1-111111-11-11-1-1-1-1-111-1-111i−ii−iii−i−i1-1iiii−i−i−i−i1-1ii−i−i11-1-11-11-1ii−i−i1-1i−i
χ101111-1-111111-11-11-1-1-1-1-111-1-111i−ii−iii−i−i1-1iiii−i−i−i−i1-1ii−i−i11-1-1-11-11−i−iii-11−ii
χ111111-1-111111-11-11-1-1-1-1-111-1-111i−ii−i−i−iii1-1−i−i−i−iiiii-11ii−i−i-1-1111-11-1ii−i−i-11−ii
χ121111-1-111111-11-11-1-1-1-1-111-1-111i−ii−i−i−iii1-1−i−i−i−iiiii-11ii−i−i-1-111-11-11−i−iii1-1i−i
χ131111-1-111111-11-11-1-1-1-1-111-1-111−ii−iiii−i−i1-1iiii−i−i−i−i-11−i−iii-1-1111-11-1−i−iii-11i−i
χ141111-1-111111-11-11-1-1-1-1-111-1-111−ii−iiii−i−i1-1iiii−i−i−i−i-11−i−iii-1-111-11-11ii−i−i1-1−ii
χ151111-1-111111-11-11-1-1-1-1-111-1-111−ii−ii−i−iii1-1−i−i−i−iiiii1-1−i−iii11-1-11-11-1−i−iii1-1−ii
χ161111-1-111111-11-11-1-1-1-1-111-1-111−ii−ii−i−iii1-1−i−i−i−iiiii1-1−i−iii11-1-1-11-11ii−i−i-11i−i
χ17222222222222-2-2-2-22222-2-2-2-2-2-2000000002-200000000000000000000002-22-20000
χ18222222222222-2-2-2-22222-2-2-2-2-2-2000000002-20000000000000000000000-22-220000
χ192222222222-2-22-2-2222-2-222-2-2-2-222-2-20000-2200000000002-22-20000000000000000
χ202222222222-2-22-2-2222-2-222-2-2-2-2-2-2220000-220000000000-22-220000000000000000
χ212222222222-2-2-222-222-2-2-2-2222200000000-2-200000000000000000022-2-200000000
χ222222222222-2-2-222-222-2-2-2-2222200000000-2-2000000000000000000-2-22200000000
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
χ24222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-2-2-1-1-1-11111000000000000
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
χ26222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111221111-1-1-1-1000000000000
χ27222222-1-1-1-1-2-22-2-22-1-111-1-1111122-2-200001-133−3−333−3−300-11-113−33−3000000000000
χ28222222-1-1-1-1-2-22-2-22-1-111-1-1111122-2-200001-1−3−333−3−33300-11-11−33−33000000000000
χ29222222-1-1-1-1-2-22-2-22-1-111-1-11111-2-22200001-133−3−333−3−3001-11-1−33−33000000000000
χ30222222-1-1-1-1-2-22-2-22-1-111-1-11111-2-22200001-1−3−333−3−333001-11-13−33−3000000000000
χ312222-2-222222-2-22-22-2-2-2-2-2-222-2-2000000002200000000000000000000002i−2i−2i2i0000
χ322222-2-222222-2-22-22-2-2-2-2-2-222-2-200000000220000000000000000000000−2i2i2i−2i0000
χ332222-2-22222-2222-2-2-2-2222222-2-22i−2i−2i2i0000-2-200000000002i−2i−2i2i0000000000000000
χ342222-2-22222-2222-2-2-2-2222222-2-2−2i2i2i−2i0000-2-20000000000−2i2i2i−2i0000000000000000
χ352222-2-22222-22-2-222-2-222-2-2-2-22200000000-220000000000000000002-2-2200000000
χ362222-2-22222-22-2-222-2-222-2-2-2-22200000000-22000000000000000000-222-200000000
χ372222-2-2-1-1-1-12-22-22-21111-1-111-1-12i−2i2i−2i2i2i−2i−2i-11−i−i−i−iiiii2-2−i−iii-1-111000000000000
χ382222-2-2-1-1-1-12-22-22-21111-1-111-1-12i−2i2i−2i−2i−2i2i2i-11iiii−i−i−i−i-22−i−iii11-1-1000000000000
χ392222-2-2-1-1-1-12-22-22-21111-1-111-1-1−2i2i−2i2i2i2i−2i−2i-11−i−i−i−iiiii-22ii−i−i11-1-1000000000000
χ402222-2-2-1-1-1-12-22-22-21111-1-111-1-1−2i2i−2i2i−2i−2i2i2i-11iiii−i−i−i−i2-2ii−i−i-1-111000000000000
χ412222-2-2-1-1-1-1-2222-2-211-1-1-1-1-1-1112i−2i−2i2i000011−i3−i3i3i3i3i3−i3−i300−iii−i−333−3000000000000
χ422222-2-2-1-1-1-1-2222-2-211-1-1-1-1-1-1112i−2i−2i2i000011i3i3−i3−i3−i3−i3i3i300−iii−i3−3−33000000000000
χ432222-2-2-1-1-1-1-2222-2-211-1-1-1-1-1-111−2i2i2i−2i000011−i3−i3i3i3i3i3−i3−i300i−i−ii3−3−33000000000000
χ442222-2-2-1-1-1-1-2222-2-211-1-1-1-1-1-111−2i2i2i−2i000011i3i3−i3−i3−i3−i3i3i300i−i−ii−333−3000000000000
χ45444444-2-2-2-244-4-4-4-4-2-2-2-222222200000000-22000000000000000000000000000000
χ46444444-2-2-2-2-4-4-444-4-2-22222-2-2-2-20000000022000000000000000000000000000000
χ474444-4-4-2-2-2-24-4-44-44222222-2-22200000000-2-2000000000000000000000000000000
χ484444-4-4-2-2-2-2-44-4-44422-2-22222-2-2000000002-2000000000000000000000000000000
χ4944-4-44-444-4-40000004-40000000000002-22-2002-22-22-22-20000000000000000000000
χ5044-4-44-444-4-40000004-4000000000000-22-2200-22-22-22-220000000000000000000000
χ5144-4-44-4-2-222000000-22000023−2323−2300002-22-200−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ5244-4-44-4-2-222000000-22000023−2323−230000-22-22001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ5344-4-44-4-2-222000000-220000−2323−232300002-22-200−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ5444-4-44-4-2-222000000-220000−2323−23230000-22-22001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ5544-4-4-4444-4-4000000-440000000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ5644-4-4-4444-4-4000000-44000000000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ5744-4-4-44-2-2220000002-2000023−23−232300002i−2i−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ5844-4-4-44-2-2220000002-2000023−23−23230000−2i2i2i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ5944-4-4-44-2-2220000002-20000−232323−2300002i−2i−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ6044-4-4-44-2-2220000002-20000−232323−230000−2i2i2i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ618-88-8008-8-8800000000000000000000000000000000000000000000000000000000
χ628-88-800-444-400000000−4i34i30000000000000000000000000000000000000000000000
χ638-88-800-444-4000000004i3−4i30000000000000000000000000000000000000000000000
χ648-8-88008-88-800000000000000000000000000000000000000000000000000000000
χ658-8-8800-44-44000000000043−4300000000000000000000000000000000000000000000
χ668-8-8800-44-440000000000−434300000000000000000000000000000000000000000000

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