Finite Group Databasebeta

← Group #10698950

Character table — Group #10698950

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order1222223444444666121212124446612121212121212121212224466668888888812121212242424242424242424242424242424248888444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ9222222222-2-222222-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2222200000000-2-2-2-200000000000000000000000000
χ10222222222-2-222222-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-200000000222200000000000000000000000000
χ112222222-2-222-2-222222222-2-222-2-2-2-222-2-2-2-2000000002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i000000000000000000
χ122222222-2-222-2-222222222-2-222-2-2-2-222-2-2-2-200000000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i000000000000000000
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-2222200000000000022-2-20000000000002222-2-2-2-20000000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-22222000000000000-2-222000000000000-2-2-2-222220000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000
χ19222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-100000000111133−3−333−3−333−3−333−3−30000000000
χ20222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1000000001111−3−333−3−333−3−333−3−3330000000000
χ21222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222111100000000-1-1-1-133−3−333−3−3−3−333−3−3330000000000
χ22222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222111100000000-1-1-1-1−3−333−3−33333−3−333−3−30000000000
χ23222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-1-11111-1-111110000−i3−i3i3i32i2i−2i−2i0000−i3−i3i3i3−i−i−i−iiiii33−3−3−3−3330000000000
χ24222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-1-11111-1-111110000−i3−i3i3i3−2i−2i2i2i0000−i3−i3i3i3iiii−i−i−i−i−3−33333−3−30000000000
χ25222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-1-11111-1-111110000i3i3−i3−i32i2i−2i−2i0000i3i3−i3−i3−i−i−i−iiiii−3−33333−3−30000000000
χ26222222-1-2-222-2-2-1-1-1-1-1-1-12-2-2-1-11111-1-111110000i3i3−i3−i3−2i−2i2i2i0000i3i3−i3−i3iiii−i−i−i−i33−3−3−3−3330000000000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-10000−i3−i3i3i3000022-2-2i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-1-1-111110000000000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-10000−i3−i3i3i30000-2-222i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31111-1-1-1-10000000000
χ29222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-10000i3i3−i3−i3000022-2-2−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-1-1-111110000000000
χ30222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-10000i3i3−i3−i30000-2-222−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31111-1-1-1-10000000000
χ312222-2-222222-2-22222222-22-2-2-222-2-2-2-222-2-20000000000000000000000000000000000000000002i−2i00
χ322222-2-222222-2-22222222-22-2-2-222-2-2-2-222-2-2000000000000000000000000000000000000000000−2i2i00
χ332222-2-2222-2-2-2-2222-2-2-2-22-22-2-222-2-222-2-2220000000000000000000000000000000000002i2i−2i−2i000000
χ342222-2-2222-2-2-2-2222-2-2-2-22-22-2-222-2-222-2-222000000000000000000000000000000000000−2i−2i2i2i000000
χ352222-2-22-2-222222222222-2-22-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000002-2
χ362222-2-22-2-222222222222-2-22-2-2-2-222-2-2-2-22200000000000000000000000000000000000000000000-22
χ372222-2-22-2-2-2-222222-2-2-2-222-2-2-2-2-2222222-2-200000000000000000000000000000000000000002-20000
χ382222-2-22-2-2-2-222222-2-2-2-222-2-2-2-2-2222222-2-20000000000000000000000000000000000000000-220000
χ3922-2-2-2222-2002-22-2-200000002-22-22-2000000002i−2i00002−22−2−i2i2−i2i22i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ4022-2-2-2222-2002-22-2-200000002-22-22-2000000002i−2i0000−22−22i2−i2i2−i22i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ4122-2-2-2222-2002-22-2-200000002-22-22-200000000−2i2i00002−22−2i2−i2i2−i2−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ4222-2-2-2222-2002-22-2-200000002-22-22-200000000−2i2i0000−22−22−i2i2−i2i2−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ4322-2-2-222-2200-222-2-200000002-2-22-220000002-2002-22-2−i2i2i2−i2−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ4422-2-2-222-2200-222-2-200000002-2-22-220000002-2002-22-2i2−i2−i2i2i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ4522-2-2-222-2200-222-2-200000002-2-22-22000000-2200-22-22−i2i2i2−i2i2−i2−i2i20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ4622-2-2-222-2200-222-2-200000002-2-22-22000000-2200-22-22i2−i2−i2i2−i2i2i2−i20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4722-2-2-22-12-2002-2-11133−3−3000-11-11-113−33−33−3002i−2i−i3i3i3−i32−22−2−i2i2−i2i2−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ4822-2-2-22-12-2002-2-11133−3−3000-11-11-113−33−33−3002i−2i−i3i3i3−i3−22−22i2−i2i2−i2−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ4922-2-2-22-12-2002-2-11133−3−3000-11-11-113−33−33−300−2i2ii3−i3−i3i32−22−2i2−i2i2−i2i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ5022-2-2-22-12-2002-2-11133−3−3000-11-11-113−33−33−300−2i2ii3−i3−i3i3−22−22−i2i2−i2i2i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ5122-2-2-22-12-2002-2-111−3−333000-11-11-11−33−33−33002i−2ii3−i3−i3i32−22−2−i2i2−i2i2−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ5222-2-2-22-12-2002-2-111−3−333000-11-11-11−33−33−33002i−2ii3−i3−i3i3−22−22i2−i2i2−i2−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ5322-2-2-22-12-2002-2-111−3−333000-11-11-11−33−33−3300−2i2i−i3i3i3−i32−22−2i2−i2i2−i2i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ5422-2-2-22-12-2002-2-111−3−333000-11-11-11−33−33−3300−2i2i−i3i3i3−i3−22−22−i2i2−i2i2i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ5522-2-2-22-1-2200-22-11133−3−3000-111-11-13−3−33−332-200-11-11−i2i2i2−i2−i2i2i2−i23−3−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ5622-2-2-22-1-2200-22-11133−3−3000-111-11-13−3−33−332-200-11-11i2−i2−i2i2i2−i2−i2i23−3−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ5722-2-2-22-1-2200-22-11133−3−3000-111-11-13−3−33−33-22001-11-1−i2i2i2−i2i2−i2−i2i2−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ5822-2-2-22-1-2200-22-11133−3−3000-111-11-13−3−33−33-22001-11-1i2−i2−i2i2−i2i2i2−i2−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ5922-2-2-22-1-2200-22-111−3−333000-111-11-1−333−33−32-200-11-11−i2i2i2−i2−i2i2i2−i2−333−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ6022-2-2-22-1-2200-22-111−3−333000-111-11-1−333−33−32-200-11-11i2−i2−i2i2i2−i2−i2i2−333−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ6122-2-2-22-1-2200-22-111−3−333000-111-11-1−333−33−3-22001-11-1−i2i2i2−i2i2−i2−i2i23−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ6222-2-2-22-1-2200-22-111−3−333000-111-11-1−333−33−3-22001-11-1i2−i2−i2i2−i2i2i2−i23−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ634444-4-4-24444-4-4-2-2-2-2-2-2-2-44-422-2-22222-2-2220000000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-4-4-2-2-222224-4422-2-222-2-222-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-4-44444-2-2-2-2-2-2-2-4-442222-2-22222-2-20000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-4-444-2-2-2222244-42222-2-2-2-2-2-2220000000000000000000000000000000000000000000000
χ6744-4-44-444-400-444-4-40000000-444-4-440000000000000000000000000000000000000000000000000000
χ6844-4-44-44-44004-44-4-40000000-44-444-40000000000000000000000000000000000000000000000000000
χ6944-4-44-4-24-400-44-2222323−23−230002-2-222-2−232323−23−23230000000000000000000000000000000000000000000000
χ7044-4-44-4-24-400-44-222−23−2323230002-2-222-223−23−232323−230000000000000000000000000000000000000000000000
χ7144-4-44-4-2-44004-4-2222323−23−230002-22-2-22−2323−232323−230000000000000000000000000000000000000000000000
χ7244-4-44-4-2-44004-4-222−23−2323230002-22-2-2223−2323−23−23230000000000000000000000000000000000000000000000
χ734-44-4004004i−4i00-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ744-44-4004004i−4i00-44-44i−4i4i−4i000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ754-44-400400−4i4i00-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ764-44-400400−4i4i00-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ778-88-800-4008i−8i004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400−8i8i004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.