Finite Group Databasebeta

← Group #10698845

Character table — Group #10698845

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order1222223444444666121212124446612121212121212121212224466668888888812121212242424242424242424242424242424248888448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111
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
χ112222222-2-222-2-222222222-2-222-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000002i−2i
χ122222222-2-222-2-222222222-2-222-2-2-2-2-2-222-2-200000000000000000000000000000000000000000000−2i2i
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000000000002i−2i00
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000000000000000−2i2i00
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
χ19222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−30000000000
χ20222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−333330000000000
χ21222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222111100000000-1-1-1-13333−3−3−3−3−3−3−3−333330000000000
χ22222222-122-2-222-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−30000000000
χ232222-2-222-2222-22222222-2-22-2-222-2-2-2-2-2-2220000000022-2-20000000022-2-222-2-2000000000000000000
χ242222-2-222-2222-22222222-2-22-2-222-2-2-2-2-2-22200000000-2-22200000000-2-222-2-222000000000000000000
χ252222-2-222-2-2-22-2222-2-2-2-222-2-2-222-2-22222-2-20000000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ262222-2-222-2-2-22-2222-2-2-2-222-2-2-222-2-22222-2-2000000000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ272222-2-22-2222-222222222-22-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000022-2-2000000
χ282222-2-22-2222-222222222-22-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000-2-222000000
χ292222-2-22-22-2-2-22222-2-2-2-22-22-2-2-2-222-2-2222200000000000000000000000000000000000000002-20000
χ302222-2-22-22-2-2-22222-2-2-2-22-22-2-2-2-222-2-222220000000000000000000000000000000000000000-220000
χ312222-2-2-12-2222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000−i3−i3i3i322-2-20000−i3−i3i3i3-1-111-1-111−i3−i3i3i3i3i3−i3−i30000000000
χ322222-2-2-12-2222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000−i3−i3i3i3-2-2220000−i3−i3i3i311-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000
χ332222-2-2-12-2222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000i3i3−i3−i322-2-20000i3i3−i3−i3-1-111-1-111i3i3−i3−i3−i3−i3i3i30000000000
χ342222-2-2-12-2222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000i3i3−i3−i3-2-2220000i3i3−i3−i311-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000
χ352222-2-2-12-2-2-22-2-1-1-1111122-211-1-111-1-1-1-1110000−i3−i3i3i300002i2i−2i−2ii3i3−i3−i333−3−3−3−333−i−iii−i−iii0000000000
χ362222-2-2-12-2-2-22-2-1-1-1111122-211-1-111-1-1-1-1110000−i3−i3i3i30000−2i−2i2i2ii3i3−i3−i3−3−33333−3−3ii−i−iii−i−i0000000000
χ372222-2-2-12-2-2-22-2-1-1-1111122-211-1-111-1-1-1-1110000i3i3−i3−i300002i2i−2i−2i−i3−i3i3i3−3−33333−3−3−i−iii−i−iii0000000000
χ382222-2-2-12-2-2-22-2-1-1-1111122-211-1-111-1-1-1-1110000i3i3−i3−i30000−2i−2i2i2i−i3−i3i3i333−3−3−3−333ii−i−iii−i−i0000000000
χ3922-2-22-222200-2-22-2-200000002-22-22-20000002-2002-22-22−22−22−22−200002−22−22−22−22−22−22−22−20000000000
χ4022-2-22-222200-2-22-2-200000002-22-22-20000002-2002-22-2−22−22−22−220000−22−22−22−22−22−22−22−220000000000
χ4122-2-22-222200-2-22-2-200000002-22-22-2000000-2200-22-222−22−2−22−2200002−22−22−22−2−22−22−22−220000000000
χ4222-2-22-222200-2-22-2-200000002-22-22-2000000-2200-22-22−22−222−22−20000−22−22−22−222−22−22−22−20000000000
χ4322-2-22-2-12200-2-2-11133−3−3000-11-11-113−33−33−32-200-11-112−22−22−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ4422-2-22-2-12200-2-2-11133−3−3000-11-11-113−33−33−32-200-11-11−22−22−22−223−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ4522-2-22-2-12200-2-2-11133−3−3000-11-11-113−33−33−3-22001-11-12−22−2−22−22−33−33ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ4622-2-22-2-12200-2-2-11133−3−3000-11-11-113−33−33−3-22001-11-1−22−222−22−2−33−33−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ4722-2-22-2-12200-2-2-111−3−333000-11-11-11−33−33−332-200-11-112−22−22−22−2−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ4822-2-22-2-12200-2-2-111−3−333000-11-11-11−33−33−332-200-11-11−22−22−22−22−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ4922-2-22-2-12200-2-2-111−3−333000-11-11-11−33−33−33-22001-11-12−22−2−22−223−33−3ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ5022-2-22-2-12200-2-2-111−3−333000-11-11-11−33−33−33-22001-11-1−22−222−22−23−33−3−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ5122-2-2-2222-200-222-2-20000000-222-2-22000000002i−2i00002−2−22−i2i2i2−i2−2i2i2i−2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000
χ5222-2-2-2222-200-222-2-20000000-222-2-22000000002i−2i0000−222−2i2−i2−i2i2−2i2i2i−2i−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000
χ5322-2-2-2222-200-222-2-20000000-222-2-2200000000−2i2i00002−2−22i2−i2−i2i22i−2i−2i2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000
χ5422-2-2-2222-200-222-2-20000000-222-2-2200000000−2i2i0000−222−2−i2i2i2−i22i−2i−2i2i−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000
χ5522-2-2-22-12-200-22-11133−3−30001-1-111-1−33−333−3002i−2ii3−i3−i3i32−2−22−i2i2i2−i2i−i−iiζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ230000000000
χ5622-2-2-22-12-200-22-11133−3−30001-1-111-1−33−333−3002i−2ii3−i3−i3i3−222−2i2−i2−i2i2i−i−ii−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ230000000000
χ5722-2-2-22-12-200-22-11133−3−30001-1-111-1−33−333−300−2i2i−i3i3i3−i32−2−22i2−i2−i2i2−iii−iζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ230000000000
χ5822-2-2-22-12-200-22-11133−3−30001-1-111-1−33−333−300−2i2i−i3i3i3−i3−222−2−i2i2i2−i2−iii−i−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ230000000000
χ5922-2-2-22-12-200-22-111−3−3330001-1-111-13−33−3−33002i−2i−i3i3i3−i32−2−22−i2i2i2−i2i−i−iiζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ70000000000
χ6022-2-2-22-12-200-22-111−3−3330001-1-111-13−33−3−33002i−2i−i3i3i3−i3−222−2i2−i2−i2i2i−i−ii−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ70000000000
χ6122-2-2-22-12-200-22-111−3−3330001-1-111-13−33−3−3300−2i2ii3−i3−i3i32−2−22i2−i2−i2i2−iii−iζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ70000000000
χ6222-2-2-22-12-200-22-111−3−3330001-1-111-13−33−3−3300−2i2ii3−i3−i3i3−222−2−i2i2i2−i2−iii−i−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ70000000000
χ63444444-2-4-444-4-4-2-2-2-2-2-2-24-4-4-2-2222222-2-2220000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-2-2-22222-444-2-22222-2-222-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-4444-44-2-2-2-2-2-2-2-44-42222-2-2-2-222220000000000000000000000000000000000000000000000
χ664444-4-4-2-44-4-4-44-2-2-222224-442222-2-222-2-2-2-20000000000000000000000000000000000000000000000
χ6744-4-44-44-4-400444-4-400000004-4-44-440000000000000000000000000000000000000000000000000000
χ6844-4-44-4-2-4-40044-2222323−23−23000-222-22-2−232323−23−23230000000000000000000000000000000000000000000000
χ6944-4-44-4-2-4-40044-222−23−232323000-222-22-223−23−232323−230000000000000000000000000000000000000000000000
χ7044-4-4-444-44004-44-4-40000000-44-444-40000000000000000000000000000000000000000000000000000
χ7144-4-4-44-2-44004-4-2222323−23−230002-22-2-2223−23−2323−23230000000000000000000000000000000000000000000000
χ7244-4-4-44-2-44004-4-222−23−2323230002-22-2-22−232323−2323−230000000000000000000000000000000000000000000000
χ734-44-4004004-400-4-444-44-400000000000000000000000000000000000000000000000000000−2i22i2000000
χ744-44-4004004-400-4-444-44-4000000000000000000000000000000000000000000000000000002i2−2i2000000
χ754-44-400400-4400-4-44-44-44000000000000000000000000000000000000000000000000000−2i22i200000000
χ764-44-400400-4400-4-44-44-440000000000000000000000000000000000000000000000000002i2−2i200000000
χ778-88-800-4008-80044-4-44-440000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400-880044-44-44-40000000000000000000000000000000000000000000000000000000000000
χ798-8-88008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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