Finite Group Databasebeta

← Group #10697952

Character table — Group #10697952

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444444444444444444444444444441616161616161616161616164848484848484848
order12223444444666121212122444444444446612121212121212121212121212121212121212121212121212124488121212122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ92222222-2-222222-2-2-2-2-2-2-2200000000-2-2222222-2-2-2-200000000000000002-20022-2-2000000000000
χ102222222-2-222222-2-2-2-2-2-2-2200000000-2-2222222-2-2-2-20000000000000000-2200-2-222000000000000
χ11222222-2222-22222222-22-2-200000000-2-2-2-222-2-222-2-20000000000000000000000000000020-20000
χ12222222-2222-22222222-22-2-200000000-2-2-2-222-2-222-2-200000000000000000000000000000-2020000
χ13222222-2-2-22-2222-2-2-2-22-22-20000000022-2-222-2-2-2-222000000000000000000000000000000002-200
χ14222222-2-2-22-2222-2-2-2-22-22-20000000022-2-222-2-2-2-22200000000000000000000000000000000-2200
χ1522222-2222-222222222-2-22-200000000-2-2-2-2-2-222-2-222000000000000000000000000000020-200000
χ1622222-2222-222222222-2-22-200000000-2-2-2-2-2-222-2-2220000000000000000000000000000-20200000
χ1722222-22-2-2-22222-2-2-2-222-2-20000000022-2-2-2-22222-2-200000000000000000000000000000000002-2
χ1822222-22-2-2-22222-2-2-2-222-2-20000000022-2-2-2-22222-2-20000000000000000000000000000000000-22
χ1922222-2-222-2-222222222-2-22000000002222-2-2-2-2-2-2-2-20000000000000000002-2000022-2-200000000
χ2022222-2-222-2-222222222-2-22000000002222-2-2-2-2-2-2-2-2000000000000000000-220000-2-22200000000
χ2122222-2-2-2-2-2-2222-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2-222-2-2-2-222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i00000000000000000000
χ2222222-2-2-2-2-2-2222-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-222-2-2-2-22222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i00000000000000000000
χ232222-1222222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ242222-1222222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ252222-1222222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-1111100000000
χ262222-1222222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-100000000
χ272222-122-2-222-1-1-11111-2-2-220000000011-1-1-1-1-1-111113333−3−3−3−33333−3−3−3−32-200-1-1113−33−300000000
χ282222-122-2-222-1-1-11111-2-2-220000000011-1-1-1-1-1-111113333−3−3−3−33333−3−3−3−3-220011-1-1−33−3300000000
χ292222-122-2-222-1-1-11111-2-2-220000000011-1-1-1-1-1-11111−3−3−3−33333−3−3−3−333332-200-1-111−33−3300000000
χ302222-122-2-222-1-1-11111-2-2-220000000011-1-1-1-1-1-11111−3−3−3−33333−3−3−3−33333-220011-1-13−33−300000000
χ312222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200000000-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3002-2−i3i3−i3i3-1-11100000000
χ322222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200000000-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300-22i3−i3i3−i311-1-100000000
χ332222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200000000-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3002-2i3−i3i3−i3-1-11100000000
χ342222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200000000-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300-22−i3i3−i3i311-1-100000000
χ352222-1-2-2-2-2-2-2-1-1-11111-22222i2i2i2i−2i−2i−2i−2i11-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000−i3i3i3−i33−3−3300000000
χ362222-1-2-2-2-2-2-2-1-1-11111-22222i2i2i2i−2i−2i−2i−2i11-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000i3−i3−i3i3−333−300000000
χ372222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i−2i−2i2i2i2i2i11-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000−i3i3i3−i3−333−300000000
χ382222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i−2i−2i2i2i2i2i11-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000i3−i3−i3i33−3−3300000000
χ394444-24-4444-4-2-2-2-2-2-2-2-44-4-4000000002222-2-222-2-222000000000000000000000000000000000000
χ404444-24-4-4-44-4-2-2-222224-44-400000000-2-222-2-22222-2-2000000000000000000000000000000000000
χ414444-2-4444-44-2-2-2-2-2-2-2-4-44-400000000222222-2-222-2-2000000000000000000000000000000000000
χ424444-2-44-4-4-44-2-2-2222244-4-400000000-2-22222-2-2-2-222000000000000000000000000000000000000
χ4344-4-4404000-4-44-40000000022-2-222-2-20000004-4000022-2-222-2-222-2-222-2-200000000000000000000
χ4444-4-4404000-4-44-400000000-2-222-2-2220000004-40000-2-222-2-222-2-222-2-22200000000000000000000
χ4544-4-440-40004-44-4000000002i2i−2i−2i−2i−2i2i2i000000-4400002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ4644-4-440-40004-44-400000000−2i−2i2i2i2i2i−2i−2i000000-440000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000
χ4744-4-4-204000-42-2223−2323−23000022-2-222-2-2000000-220023−23−1+3−1+31−31−3−1−3−1−31+31+3−1+3−1+31−31−3−1−3−1−31+31+300000000000000000000
χ4844-4-4-204000-42-2223−2323−230000-2-222-2-222000000-220023−231−31−3−1+3−1+31+31+3−1−3−1−31−31−3−1+3−1+31+31+3−1−3−1−300000000000000000000
χ4944-4-4-204000-42-22−2323−2323000022-2-222-2-2000000-2200−2323−1−3−1−31+31+3−1+3−1+31−31−3−1−3−1−31+31+3−1+3−1+31−31−300000000000000000000
χ5044-4-4-204000-42-22−2323−23230000-2-222-2-222000000-2200−23231+31+3−1−3−1−31−31−3−1+3−1+31+31+3−1−3−1−31−31−3−1+3−1+300000000000000000000
χ5144-4-4-20-400042-2223−2323−2300002i2i−2i−2i−2i−2i2i2i0000002-200−2323−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ5244-4-4-20-400042-2223−2323−230000−2i−2i2i2i2i2i−2i−2i0000002-200−2323ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000
χ5344-4-4-20-400042-22−2323−232300002i2i−2i−2i−2i−2i2i2i0000002-20023−23ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ5444-4-4-20-400042-22−2323−23230000−2i−2i2i2i2i2i−2i−2i0000002-20023−23−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000
χ554-44-444000-40-4-44000000002-22-22-22-200004-40000002-22-22-22-22-22-22-22-200000000000000000000
χ564-44-444000-40-4-4400000000-22-22-22-2200004-4000000-22-22-22-22-22-22-22-2200000000000000000000
χ574-44-44-400040-4-44000000002i−2i2i−2i−2i2i−2i2i0000-440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ584-44-44-400040-4-4400000000−2i2i−2i2i2i−2i2i−2i0000-44000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000
χ594-44-4-24000-4022-223−23−232300002-22-22-22-20000-220023−2300−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+300000000000000000000
χ604-44-4-24000-4022-223−23−23230000-22-22-22-220000-220023−23001−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−300000000000000000000
χ614-44-4-24000-4022-2−232323−2300002-22-22-22-20000-2200−232300−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−300000000000000000000
χ624-44-4-24000-4022-2−232323−230000-22-22-22-220000-2200−2323001+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+300000000000000000000
χ634-44-4-2-40004022-223−23−232300002i−2i2i−2i−2i2i−2i2i00002-200−232300−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ644-44-4-2-40004022-223−23−23230000−2i2i−2i2i2i−2i2i−2i00002-200−232300ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000
χ654-44-4-2-40004022-2−232323−2300002i−2i2i−2i−2i2i−2i2i00002-20023−2300ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ664-44-4-2-40004022-2−232323−230000−2i2i−2i2i2i−2i2i−2i00002-20023−2300−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000
χ674-4-444004-4004-4-444-4-400002-2-222-2-220000000000002-2-222-2-222-2-222-2-2200000000000000000000
χ684-4-444004-4004-4-444-4-40000-222-2-222-2000000000000-222-2-222-2-222-2-222-200000000000000000000
χ694-4-44400-44004-4-4-4-44400002i−2i−2i2i−2i2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ704-4-44400-44004-4-4-4-4440000−2i2i2i−2i2i−2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ714-4-44-2004-400-222-2-22200002-2-222-2-22−2i32i3−2i32i300000000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i300000000000000000000
χ724-4-44-2004-400-222-2-22200002-2-222-2-222i3−2i32i3−2i300000000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i300000000000000000000
χ734-4-44-2004-400-222-2-2220000-222-2-222-2−2i32i3−2i32i3000000001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i300000000000000000000
χ744-4-44-2004-400-222-2-2220000-222-2-222-22i3−2i32i3−2i3000000001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i300000000000000000000
χ754-4-44-200-4400-22222-2-200002i−2i−2i2i−2i2i2i−2i−2i32i32i3−2i3000000002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ700000000000000000000
χ764-4-44-200-4400-22222-2-200002i−2i−2i2i−2i2i2i−2i2i3−2i3−2i32i3000000002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ1100000000000000000000
χ774-4-44-200-4400-22222-2-20000−2i2i2i−2i2i−2i−2i2i−2i32i32i3−2i300000000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ112ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ700000000000000000000
χ784-4-44-200-4400-22222-2-20000−2i2i2i−2i2i−2i−2i2i2i3−2i3−2i32i300000000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ72ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ1100000000000000000000

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