Finite Group Databasebeta

← Group #10695413

Character table — Group #10695413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888888888888888242424242424242448484848
order1222222222223666666644446666121212121212121222446666888888881212121224242424242424242424242424242424444444442444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ922222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2222200000000-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-20000000022220000000000000000000000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1000000000000
χ15222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−3000000000000
χ16222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−33333000000000000
χ17222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222111100000000-1-1-1-13333−3−3−3−3−3−3−3−33333000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−3000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000000000200-2
χ2022222222-2-2-2-2222222222-22-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000000000-2002
χ2122222222-2-2-2-222222222-22-22-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000002-20
χ2222222222-2-2-2-222222222-22-22-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000-220
χ23222-2-2-2-2222-2-22222-2-2-2-2000022-2-200000000002i−2i000022−2−2−i2−i2i2i22i2i−2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ24222-2-2-2-2222-2-22222-2-2-2-2000022-2-200000000002i−2i0000−2−222i2i2−i2−i22i2i−2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ25222-2-2-2-2222-2-22222-2-2-2-2000022-2-20000000000−2i2i000022−2−2i2i2−i2−i2−2i−2i2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ26222-2-2-2-2222-2-22222-2-2-2-2000022-2-20000000000−2i2i0000−2−222−i2−i2i2i2−2i−2i2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ27222-2-2-2-2222-2-2-1-1-1-111110000-1-1113−33−33−33−3002i−2i−i3−i3i3i322−2−2−i2−i2i2i2−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ28222-2-2-2-2222-2-2-1-1-1-111110000-1-1113−33−33−33−3002i−2i−i3−i3i3i3−2−222i2i2−i2−i2−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ29222-2-2-2-2222-2-2-1-1-1-111110000-1-1113−33−33−33−300−2i2ii3i3−i3−i322−2−2i2i2−i2−i2ii−i−iζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ30222-2-2-2-2222-2-2-1-1-1-111110000-1-1113−33−33−33−300−2i2ii3i3−i3−i3−2−222−i2−i2i2i2ii−i−i−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ31222-2-2-2-2222-2-2-1-1-1-111110000-1-111−33−33−33−33002i−2ii3i3−i3−i322−2−2−i2−i2i2i2−i−iiiζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ32222-2-2-2-2222-2-2-1-1-1-111110000-1-111−33−33−33−33002i−2ii3i3−i3−i3−2−222i2i2−i2−i2−i−iii−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ33222-2-2-2-2222-2-2-1-1-1-111110000-1-111−33−33−33−3300−2i2i−i3−i3i3i322−2−2i2i2−i2−i2ii−i−iζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ34222-2-2-2-2222-2-2-1-1-1-111110000-1-111−33−33−33−3300−2i2i−i3−i3i3i3−2−222−i2−i2i2i2ii−i−i−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ352-2-222-2-222-22-222-2-2-2-22222-2-22-22-22222-2-2-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ362-2-222-2-222-22-222-2-2-2-22222-2-22-22-22222-2-2-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ372-2-222-2-222-22-222-2-2-2-222-2-2222-22-2-2-2-2-22222000000002-22-2000000002-22-22-22-200000000000000000000
χ382-2-222-2-222-22-222-2-2-2-222-2-2222-22-2-2-2-2-2222200000000-22-2200000000-22-22-22-2200000000000000000000
χ392-2-222-2-222-22-2-1-11111-1-122-2-2-11-11-1-1-1-111110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i33−33−3−33−33−ii−ii−ii−ii000000000000
χ402-2-222-2-222-22-2-1-11111-1-122-2-2-11-11-1-1-1-111110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−33−333−33−3i−ii−ii−ii−i000000000000
χ412-2-222-2-222-22-2-1-11111-1-122-2-2-11-11-1-1-1-111110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−33−333−33−3−ii−ii−ii−ii000000000000
χ422-2-222-2-222-22-2-1-11111-1-122-2-2-11-11-1-1-1-111110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i33−33−3−33−33i−ii−ii−ii−i000000000000
χ432-2-222-2-222-22-2-1-11111-1-1-2-222-11-111111-1-1-1-10000−i3i3−i3i32-22-20000i3−i3i3−i3-11-11-11-11−i3i3−i3i3i3−i3i3−i3000000000000
χ442-2-222-2-222-22-2-1-11111-1-1-2-222-11-111111-1-1-1-10000−i3i3−i3i3-22-220000i3−i3i3−i31-11-11-11-1i3−i3i3−i3−i3i3−i3i3000000000000
χ452-2-222-2-222-22-2-1-11111-1-1-2-222-11-111111-1-1-1-10000i3−i3i3−i32-22-20000−i3i3−i3i3-11-11-11-11i3−i3i3−i3−i3i3−i3i3000000000000
χ462-2-222-2-222-22-2-1-11111-1-1-2-222-11-111111-1-1-1-10000i3−i3i3−i3-22-220000−i3i3−i3i31-11-11-11-1−i3i3−i3i3i3−i3i3−i3000000000000
χ472-2-222-2-22-22-2222-2-2-2-2222-2-22-22-2222-2-2-2-222000000000000000000000000000000000000000022-2-20000
χ482-2-222-2-22-22-2222-2-2-2-2222-2-22-22-2222-2-2-2-2220000000000000000000000000000000000000000-2-2220000
χ492-2-222-2-22-22-2222-2-2-2-222-222-2-22-22-2-22222-2-200000000000000000000000000000000000022-2-200000000
χ502-2-222-2-22-22-2222-2-2-2-222-222-2-22-22-2-22222-2-2000000000000000000000000000000000000-2-22200000000
χ512-2-2-2-22222-2-2222-2-222-2-200002-2-22000000002-2002-2-222−2−22−222−200002−2−222−2−22−222−2−222−2000000000000
χ522-2-2-2-22222-2-2222-2-222-2-200002-2-22000000002-2002-2-22−222−22−2−220000−222−2−222−22−2−222−2−22000000000000
χ532-2-2-2-22222-2-2222-2-222-2-200002-2-2200000000-2200-222-22−2−222−2−2200002−2−222−2−222−2−222−2−22000000000000
χ542-2-2-2-22222-2-2222-2-222-2-200002-2-2200000000-2200-222-2−222−2−222−20000−222−2−222−2−222−2−222−2000000000000
χ552-2-2-2-22222-2-22-1-111-1-1110000-111-13−33−3−33−332-200-111-12−2−22−222−23−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ562-2-2-2-22222-2-22-1-111-1-1110000-111-13−33−3−33−332-200-111-1−222−22−2−223−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ572-2-2-2-22222-2-22-1-111-1-1110000-111-13−33−3−33−33-22001-1-112−2−222−2−22−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ582-2-2-2-22222-2-22-1-111-1-1110000-111-13−33−3−33−33-22001-1-11−222−2−222−2−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ592-2-2-2-22222-2-22-1-111-1-1110000-111-1−33−333−33−32-200-111-12−2−22−222−2−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ602-2-2-2-22222-2-22-1-111-1-1110000-111-1−33−333−33−32-200-111-1−222−22−2−22−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ612-2-2-2-22222-2-22-1-111-1-1110000-111-1−33−333−33−3-22001-1-112−2−222−2−223−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ622-2-2-2-22222-2-22-1-111-1-1110000-111-1−33−333−33−3-22001-1-11−222−2−222−23−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ6344444444-4-4-4-4-2-2-2-2-2-2-2-24-44-42222-2-222-2-222000000000000000000000000000000000000000000000000
χ6444444444-4-4-4-4-2-2-2-2-2-2-2-2-44-44222222-2-222-2-2000000000000000000000000000000000000000000000000
χ65444-4-4-4-44-4-4444444-4-4-4-40000-4-44400000000000000000000000000000000000000000000000000000000
χ66444-4-4-4-44-4-444-2-2-2-22222000022-2-223−23−232323−23−2323000000000000000000000000000000000000000000000000
χ67444-4-4-4-44-4-444-2-2-2-22222000022-2-2−232323−23−232323−23000000000000000000000000000000000000000000000000
χ6844-44-44-4-400004-44-44-44-400000000000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ6944-44-44-4-400004-44-44-44-40000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ7044-4-44-44-400004-44-4-44-44000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ7144-4-44-44-400004-44-4-44-4400000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ724-444-4-44-400004-4-44-444-400000000000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ734-444-4-44-400004-4-44-444-40000000000000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ744-44-444-4-400004-4-444-4-44000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ754-44-444-4-400004-4-444-4-4400000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ764-4-444-4-44-44-44-2-22222-2-24-4-442-22-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ774-4-444-4-44-44-44-2-22222-2-2-444-42-22-222-2-2-2-222000000000000000000000000000000000000000000000000
χ784-4-4-4-4444-444-444-4-444-4-40000-444-400000000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-444-4-2-222-2-22200002-2-2223−23−2323−232323−23000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-444-4-2-222-2-22200002-2-22−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ8188-88-88-8-80000-44-44-44-440000000000000000000000000000000000000000000000000000000000000000
χ8288-8-88-88-80000-44-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ838-888-8-88-80000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-80000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000

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