Finite Group Databasebeta

← Group #10697548

Character table — Group #10697548

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order1222223444444666121212124446612121212121212121212224466668888888812121212242424242424242424242424242424244444222488
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
χ92222222222-2-22222-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2222200000000-2-2-2-200000000000000000000000000
χ102222222222-2-22222-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-200000000222200000000000000000000000000
χ112222222-2-2-222-22222222-22-222-2-2-2-2-2-222-2-200000000000000000000000000000000000000002-20000
χ122222222-2-2-222-22222222-22-222-2-2-2-2-2-222-2-20000000000000000000000000000000000000000-220000
χ132222222-2-2-2-2-2-2222-2-2-2-22-2222-2-2-2-222-2-22200000000000000000000000000000000000022-2-2000000
χ142222222-2-2-2-2-2-2222-2-2-2-22-2222-2-2-2-222-2-222000000000000000000000000000000000000-2-222000000
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
χ19222222-1222-2-22-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−30000000000
χ20222222-1222-2-22-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−333330000000000
χ21222222-1222-2-22-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222111100000000-1-1-1-13333−3−3−3−3−3−3−3−333330000000000
χ22222222-1222-2-22-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−30000000000
χ232222-2-2222-222-22222222-2-22-2-222-2-2-2-2-2-2220000000022-2-20000000022-2-222-2-2000000000000000000
χ242222-2-2222-222-22222222-2-22-2-222-2-2-2-2-2-22200000000-2-22200000000-2-222-2-222000000000000000000
χ252222-2-2222-2-2-2-2222-2-2-2-222-2-2-222-2-22222-2-20000000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ262222-2-2222-2-2-2-2222-2-2-2-222-2-2-222-2-22222-2-2000000000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ272222-2-22-2-2222222222222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000002-200
χ282222-2-22-2-2222222222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000-2200
χ292222-2-22-2-22-2-22222-2-2-2-2-222-2-2-2-222-2-22222000000000000000000000000000000000000000000002-2
χ302222-2-22-2-22-2-22222-2-2-2-2-222-2-2-2-222-2-2222200000000000000000000000000000000000000000000-22
χ312222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000−i3−i3i3i322-2-20000−i3−i3i3i3-1-111-1-111−i3−i3i3i3i3i3−i3−i30000000000
χ322222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000−i3−i3i3i3-2-2220000−i3−i3i3i311-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000
χ332222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000i3i3−i3−i322-2-20000i3i3−i3−i3-1-111-1-111i3i3−i3−i3−i3−i3i3i30000000000
χ342222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-1111111-1-10000i3i3−i3−i3-2-2220000i3i3−i3−i311-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000
χ352222-2-2-122-2-2-2-2-1-1-1111122-211-1-111-1-1-1-1110000−i3−i3i3i300002i2i−2i−2ii3i3−i3−i333−3−3−3−333−i−iii−i−iii0000000000
χ362222-2-2-122-2-2-2-2-1-1-1111122-211-1-111-1-1-1-1110000−i3−i3i3i30000−2i−2i2i2ii3i3−i3−i3−3−33333−3−3ii−i−iii−i−i0000000000
χ372222-2-2-122-2-2-2-2-1-1-1111122-211-1-111-1-1-1-1110000i3i3−i3−i300002i2i−2i−2i−i3−i3i3i3−3−33333−3−3−i−iii−i−iii0000000000
χ382222-2-2-122-2-2-2-2-1-1-1111122-211-1-111-1-1-1-1110000i3i3−i3−i30000−2i−2i2i2i−i3−i3i3i333−3−3−3−333ii−i−iii−i−i0000000000
χ392-2-222-222-2200-22-2-200000002-22-22-2000000002i−2i00002−22−2−i2i2−i2i22i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ402-2-222-222-2200-22-2-200000002-22-22-2000000002i−2i0000−22−22i2−i2i2−i22i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ412-2-222-222-2200-22-2-200000002-22-22-200000000−2i2i00002−22−2i2−i2i2−i2−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ422-2-222-222-2200-22-2-200000002-22-22-200000000−2i2i0000−22−22−i2i2−i2i2−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ432-2-222-2-12-2200-2-11133−3−3000-11-11-113−33−33−3002i−2i−i3i3−i3i32−22−2−i2i2−i2i2−ii−iiζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230000000000
χ442-2-222-2-12-2200-2-11133−3−3000-11-11-113−33−33−3002i−2i−i3i3−i3i3−22−22i2−i2i2−i2−ii−ii−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230000000000
χ452-2-222-2-12-2200-2-11133−3−3000-11-11-113−33−33−300−2i2ii3−i3i3−i32−22−2i2−i2i2−i2i−ii−iζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230000000000
χ462-2-222-2-12-2200-2-11133−3−3000-11-11-113−33−33−300−2i2ii3−i3i3−i3−22−22−i2i2−i2i2i−ii−i−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230000000000
χ472-2-222-2-12-2200-2-111−3−333000-11-11-11−33−33−33002i−2ii3−i3i3−i32−22−2−i2i2−i2i2−ii−iiζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70000000000
χ482-2-222-2-12-2200-2-111−3−333000-11-11-11−33−33−33002i−2ii3−i3i3−i3−22−22i2−i2i2−i2−ii−ii−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70000000000
χ492-2-222-2-12-2200-2-111−3−333000-11-11-11−33−33−3300−2i2i−i3i3−i3i32−22−2i2−i2i2−i2i−ii−iζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70000000000
χ502-2-222-2-12-2200-2-111−3−333000-11-11-11−33−33−3300−2i2i−i3i3−i3i3−22−22−i2i2−i2i2i−ii−i−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70000000000
χ512-2-22-2222-2-20022-2-20000000-222-2-220000002-2002-2-222−2−22−222−200002−2−222−2−22−222−2−222−20000000000
χ522-2-22-2222-2-20022-2-20000000-222-2-220000002-2002-2-22−222−22−2−220000−222−2−222−22−2−222−2−220000000000
χ532-2-22-2222-2-20022-2-20000000-222-2-22000000-2200-222-22−2−222−2−2200002−2−222−2−222−2−222−2−220000000000
χ542-2-22-2222-2-20022-2-20000000-222-2-22000000-2200-222-2−222−2−222−20000−222−2−222−2−222−2−222−20000000000
χ552-2-22-22-12-2-2002-11133−3−30001-1-111-1−33−333−32-200-111-12−2−22−222−23−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ230000000000
χ562-2-22-22-12-2-2002-11133−3−30001-1-111-1−33−333−32-200-111-1−222−22−2−223−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000
χ572-2-22-22-12-2-2002-11133−3−30001-1-111-1−33−333−3-22001-1-112−2−222−2−22−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000
χ582-2-22-22-12-2-2002-11133−3−30001-1-111-1−33−333−3-22001-1-11−222−2−222−2−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ230000000000
χ592-2-22-22-12-2-2002-111−3−3330001-1-111-13−33−3−332-200-111-12−2−22−222−2−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ70000000000
χ602-2-22-22-12-2-2002-111−3−3330001-1-111-13−33−3−332-200-111-1−222−22−2−22−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ70000000000
χ612-2-22-22-12-2-2002-111−3−3330001-1-111-13−33−3−33-22001-1-112−2−222−2−223−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ70000000000
χ622-2-22-22-12-2-2002-111−3−3330001-1-111-13−33−3−33-22001-1-11−222−2−222−23−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ70000000000
χ63444444-2-4-4-444-4-2-2-2-2-2-2-2-44-4-2-2222222-2-2220000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-2-2-222224-44-2-22222-2-222-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-4-44444-2-2-2-2-2-2-24-4-42222-2-2-2-222220000000000000000000000000000000000000000000000
χ664444-4-4-2-4-44-4-44-2-2-22222-4442222-2-222-2-2-2-20000000000000000000000000000000000000000000000
χ674-44-40040004-40-4-444-44-40000000000000000000000000000000000000000000000000002-22-2000000
χ684-44-40040004-40-4-444-44-4000000000000000000000000000000000000000000000000000-22-22000000
χ694-44-4004000-440-4-44-44-440000000000000000000000000000000000000000000000000002-2-22000000
χ704-44-4004000-440-4-44-44-44000000000000000000000000000000000000000000000000000-222-2000000
χ714-4-444-44-44-40044-4-400000004-4-44-440000000000000000000000000000000000000000000000000000
χ724-4-444-4-2-44-4004-2222323−23−23000-222-22-2−232323−23−23230000000000000000000000000000000000000000000000
χ734-4-444-4-2-44-4004-222−23−232323000-222-22-223−23−232323−230000000000000000000000000000000000000000000000
χ744-4-44-444-44400-44-4-40000000-44-444-40000000000000000000000000000000000000000000000000000
χ754-4-44-44-2-44400-4-2222323−23−230002-22-2-2223−23−2323−23230000000000000000000000000000000000000000000000
χ764-4-44-44-2-44400-4-222−23−2323230002-22-2-22−232323−2323−230000000000000000000000000000000000000000000000
χ7788-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ7988-8-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40008-8044-4-44-440000000000000000000000000000000000000000000000000000000000000
χ818-88-800-4000-88044-44-44-40000000000000000000000000000000000000000000000000000000000000

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