Finite Group Databasebeta

← Group #10698517

Character table — Group #10698517

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888888888888888242424242424242448484848
order12222222222236666666444466661212121212121212444488888888121212121212121224242424242424242424242424242424444444442244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ922222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-222220000000000000000000000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000
χ15222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3000000000000
χ16222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333000000000000
χ17222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000020-20
χ2022222222-2-2-2-2222222222-22-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000000000-2020
χ2122222222-2-2-2-222222222-22-22-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000020-2
χ2222222222-2-2-2-222222222-22-22-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000-202
χ2322-22-2-22-222-2-2222-2-22-2-2000022-2-200000000002-2−i2−i2i2i2−i2−i2i2i2000022-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2422-22-2-22-222-2-2222-2-22-2-2000022-2-200000000002-2i2i2−i2−i2i2i2−i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2522-22-2-22-222-2-2222-2-22-2-2000022-2-20000000000-22−i2−i2i2i2i2i2−i2−i20000-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-22-2-22-222-2-2222-2-22-2-2000022-2-20000000000-22i2i2−i2−i2−i2−i2i2i20000-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2722-22-2-22-222-2-2-1-1-111-1110000-1-1113−33−33−33−3002-2−i2−i2i2i2−i2−i2i2i233−3−3-1-111ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2822-22-2-22-222-2-2-1-1-111-1110000-1-1113−33−33−33−3002-2i2i2−i2−i2i2i2−i2−i233−3−3-1-111−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2922-22-2-22-222-2-2-1-1-111-1110000-1-1113−33−33−33−300-22−i2−i2i2i2i2i2−i2−i2−3−33311-1-1ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ3022-22-2-22-222-2-2-1-1-111-1110000-1-1113−33−33−33−300-22i2i2−i2−i2−i2−i2i2i2−3−33311-1-1−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ3122-22-2-22-222-2-2-1-1-111-1110000-1-111−33−33−33−33002-2−i2−i2i2i2−i2−i2i2i2−3−333-1-111ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ3222-22-2-22-222-2-2-1-1-111-1110000-1-111−33−33−33−33002-2i2i2−i2−i2i2i2−i2−i2−3−333-1-111−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ3322-22-2-22-222-2-2-1-1-111-1110000-1-111−33−33−33−3300-22−i2−i2i2i2i2i2−i2−i233−3−311-1-1ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ3422-22-2-22-222-2-2-1-1-111-1110000-1-111−33−33−33−3300-22i2i2−i2−i2−i2−i2i2i233−3−311-1-1−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ352-22-22-22-22-22-222-22-2-22-22-2-222-22-222-2-2-2-22200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ362-22-22-22-22-22-222-22-2-22-22-2-222-22-222-2-2-2-2220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ372-22-22-22-22-22-222-22-2-22-2-222-22-22-2-2-22222-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ382-22-22-22-22-22-222-22-2-22-2-222-22-22-2-2-22222-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ392-22-22-22-22-22-2-1-11-111-112-2-22-11-11-1-11111-1-100002i−2i2i−2i00003−33−33−33−3−ii−ii−ii−ii−i3i3−i3i3i3−i3i3−i3000000000000
χ402-22-22-22-22-22-2-1-11-111-112-2-22-11-11-1-11111-1-100002i−2i2i−2i0000−33−33−33−33−ii−ii−ii−iii3−i3i3−i3−i3i3−i3i3000000000000
χ412-22-22-22-22-22-2-1-11-111-112-2-22-11-11-1-11111-1-10000−2i2i−2i2i00003−33−33−33−3i−ii−ii−ii−ii3−i3i3−i3−i3i3−i3i3000000000000
χ422-22-22-22-22-22-2-1-11-111-112-2-22-11-11-1-11111-1-10000−2i2i−2i2i0000−33−33−33−33i−ii−ii−ii−i−i3i3−i3i3i3−i3i3−i3000000000000
χ432-22-22-22-22-22-2-1-11-111-11-222-2-11-1111-1-1-1-111000000002i−2i2i−2i3−33−3−33−33i3−i3i3−i3−i3i3−i3i3−ii−ii−ii−ii000000000000
χ442-22-22-22-22-22-2-1-11-111-11-222-2-11-1111-1-1-1-111000000002i−2i2i−2i−33−333−33−3−i3i3−i3i3i3−i3i3−i3−ii−ii−ii−ii000000000000
χ452-22-22-22-22-22-2-1-11-111-11-222-2-11-1111-1-1-1-11100000000−2i2i−2i2i3−33−3−33−33−i3i3−i3i3i3−i3i3−i3i−ii−ii−ii−i000000000000
χ462-22-22-22-22-22-2-1-11-111-11-222-2-11-1111-1-1-1-11100000000−2i2i−2i2i−33−333−33−3i3−i3i3−i3−i3i3−i3i3i−ii−ii−ii−i000000000000
χ472-22-22-22-2-22-2222-22-2-22-222-2-2-22-222222-2-2-2-20000000000000000000000000000000000002i2i−2i−2i00000000
χ482-22-22-22-2-22-2222-22-2-22-222-2-2-22-222222-2-2-2-2000000000000000000000000000000000000−2i−2i2i2i00000000
χ492-22-22-22-2-22-2222-22-2-22-2-2-222-22-22-2-2-2-22222000000000000000000000000000000000000000022-2-20000
χ502-22-22-22-2-22-2222-22-2-22-2-2-222-22-22-2-2-2-222220000000000000000000000000000000000000000-2-2220000
χ512-2-2-2-22222-2-2222-2-22-2-2200002-2-22000000002-2002−2−222−2−22-222-200002−2−222−2−222−2−222−2−22000000000000
χ522-2-2-2-22222-2-2222-2-22-2-2200002-2-22000000002-200−222−2−222−2-222-20000−222−2−222−2−222−2−222−2000000000000
χ532-2-2-2-22222-2-2222-2-22-2-2200002-2-2200000000-22002−2−22−222−22-2-2200002−2−222−2−22−222−2−222−2000000000000
χ542-2-2-2-22222-2-2222-2-22-2-2200002-2-2200000000-2200−222−22−2−222-2-220000−222−2−222−22−2−222−2−22000000000000
χ552-2-2-2-22222-2-22-1-111-111-10000-111-13−3−33−333−32-2002−2−222−2−221-1-113−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ562-2-2-2-22222-2-22-1-111-111-10000-111-13−3−33−333−32-200−222−2−222−21-1-113−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ572-2-2-2-22222-2-22-1-111-111-10000-111-13−3−33−333−3-22002−2−22−222−2-111-1−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ582-2-2-2-22222-2-22-1-111-111-10000-111-13−3−33−333−3-2200−222−22−2−22-111-1−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ592-2-2-2-22222-2-22-1-111-111-10000-111-1−333−33−3−332-2002−2−222−2−221-1-11−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ602-2-2-2-22222-2-22-1-111-111-10000-111-1−333−33−3−332-200−222−2−222−21-1-11−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ612-2-2-2-22222-2-22-1-111-111-10000-111-1−333−33−3−33-22002−2−22−222−2-111-13−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ622-2-2-2-22222-2-22-1-111-111-10000-111-1−333−33−3−33-2200−222−22−2−22-111-13−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−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
χ65444-4-4-4-4400004-4444-4-4-4000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ66444-4-4-4-4400004-4444-4-4-400000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ6744-44-4-44-4-4-444444-4-44-4-40000-4-44400000000000000000000000000000000000000000000000000000000
χ6844-44-4-44-4-4-444-2-2-222-222000022-2-223−23−232323−23−2323000000000000000000000000000000000000000000000000
χ6944-44-4-44-4-4-444-2-2-222-222000022-2-2−232323−23−232323−23000000000000000000000000000000000000000000000000
χ7044-4-444-4-400004-44-4-4-44400000000000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ7144-4-444-4-400004-44-4-4-4440000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ724-444-44-4-400004-4-44-44-44000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ734-444-44-4-400004-4-44-44-4400000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ744-44-44-44-4-44-44-2-22-222-2244-4-42-22-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ754-44-44-44-4-44-44-2-22-222-22-4-4442-22-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ764-4-444-4-4400004-4-4-4444-400000000000000000000000000000000000000000000000000002-2-2200000000
χ774-4-444-4-4400004-4-4-4444-40000000000000000000000000000000000000000000000000000-222-200000000
χ784-4-4-4-4444-444-444-4-44-4-440000-444-400000000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-444-4-2-222-222-200002-2-2223−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-444-4-2-222-222-200002-2-22−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ81888-8-8-8-880000-44-4-4-44440000000000000000000000000000000000000000000000000000000000000000
χ8288-8-888-8-80000-44-4444-4-40000000000000000000000000000000000000000000000000000000000000000
χ838-888-88-8-80000-444-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-880000-4444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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