Finite Group Databasebeta

← Group #10697140

Character table — Group #10697140

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242444881212121224242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2-2-2-2-2222-2-2-2-22-22200000000-2-22222-2-2-2-20000000000000000002i−2i00002i2i−2i−2i000000000000
χ10222222222-2-2-2-2-2-2222-2-2-2-22-22200000000-2-22222-2-2-2-2000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ112222222-2-222-2-2222222222-2-2220000000022-2-2-2-2-2-2-2-20000000000000000000000000000000022-2-20000
χ122222222-2-222-2-2222222222-2-2220000000022-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2220000
χ132222222-2-2-2-222-2-2222-2-2-2-2-222200000000-2-2-2-2-2-222220000000000000000000000000000000000002-200
χ142222222-2-2-2-222-2-2222-2-2-2-2-222200000000-2-2-2-2-2-22222000000000000000000000000000000000000-2200
χ15222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-122-2-2-2-2-2-2-1-1-111112-2-1-10000000011-1-1-1-1111133333333−3−3−3−3−3−3−3−3002i−2i−i3−i3i3i3−i−iii000000000000
χ20222222-122-2-2-2-2-2-2-1-1-111112-2-1-10000000011-1-1-1-1111133333333−3−3−3−3−3−3−3−300−2i2ii3i3−i3−i3ii−i−i000000000000
χ21222222-122-2-2-2-2-2-2-1-1-111112-2-1-10000000011-1-1-1-11111−3−3−3−3−3−3−3−333333333002i−2ii3i3−i3−i3−i−iii000000000000
χ22222222-122-2-2-2-2-2-2-1-1-111112-2-1-10000000011-1-1-1-11111−3−3−3−3−3−3−3−33333333300−2i2i−i3−i3i3i3ii−i−i000000000000
χ232222-2-222222-2-2-2-22222222-22-2-22222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ242222-2-222222-2-2-2-22222222-22-2-2-2-2-2-22222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ252222-2-2222-2-22222222-2-2-2-2-2-2-2-2000000002222-2-222-2-200000000000000002-2002-22-20000000000000000
χ262222-2-2222-2-22222222-2-2-2-2-2-2-2-2000000002222-2-222-2-20000000000000000-2200-22-220000000000000000
χ272222-2-22-2-22222-2-222222222-2-2-200000000-2-2-2-22222-2-2000000000000000000000000000022-2-200000000
χ282222-2-22-2-22222-2-222222222-2-2-200000000-2-2-2-22222-2-20000000000000000000000000000-2-22200000000
χ292222-2-22-2-2-2-2-2-222222-2-2-2-222-2-20000000022-2-222-2-222000000000000000000000000000000000000002-2
χ302222-2-22-2-2-2-2-2-222222-2-2-2-222-2-20000000022-2-222-2-22200000000000000000000000000000000000000-22
χ312222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-22112222-2-2-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000−i3i3i3−i3−i3i3−i3i3000000000000
χ322222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-22112222-2-2-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000i3−i3−i3i3i3−i3i3−i3000000000000
χ332222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-2211-2-2-2-2222211-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3i3−i3000000000000
χ342222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-2211-2-2-2-2222211-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3−i3i3000000000000
χ352222-2-2-122-2-22222-1-1-11111-2-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−333332-200-11-113−3−33000000000000
χ362222-2-2-122-2-22222-1-1-11111-2-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−33333-22001-11-1−333−3000000000000
χ372222-2-2-122-2-22222-1-1-11111-2-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−32-200-11-11−333−3000000000000
χ382222-2-2-122-2-22222-1-1-11111-2-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−3-22001-11-13−3−33000000000000
χ392-2-222-22002-2002-22-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−2000000000000−i2i2−i2i2002i−2i0000
χ402-2-222-22002-2002-22-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−2000000000000i2−i2i2−i200−2i2i0000
χ412-2-222-22002-2002-22-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−222000000000000−i2i2−i2i200−2i2i0000
χ422-2-222-22002-2002-22-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−222000000000000i2−i2i2−i2002i−2i0000
χ432-2-22-222002-200-222-2-222-2-200-2222−2−2−2−222-220000000022−2−2−2−22222−2−2−2−222000000000000−i2i2i2−i22i−2i000000
χ442-2-22-222002-200-222-2-222-2-200-2222−2−2−2−222-220000000022−2−2−2−22222−2−2−2−222000000000000i2−i2−i2i2−2i2i000000
χ452-2-22-222002-200-222-2-222-2-200-22−2−22222−2−2-2200000000−2−22222−2−2−2−22222−2−2000000000000−i2i2i2−i2−2i2i000000
χ462-2-22-222002-200-222-2-222-2-200-22−2−22222−2−2-2200000000−2−22222−2−2−2−22222−2−2000000000000i2−i2−i2i22i−2i000000
χ47444444-2-4-444-4-444-2-2-2-2-2-2-2-4-4-2-200000000-2-2222222220000000000000000000000000000000000000000
χ48444444-2-4-4-4-444-4-4-2-2-22222-44-2-200000000222222-2-2-2-20000000000000000000000000000000000000000
χ494444-4-4-2-4-44444-4-4-2-2-2-2-2-2-24-422000000002222-2-2-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4-4-4-4-4-444-2-2-22222442200000000-2-222-2-222-2-20000000000000000000000000000000000000000
χ5144-4-400400004-400-44-4000000002-22-22-22-20000004-4002-22-22-22-22-22-22-22-2000000000000000000000000
χ5244-4-400400004-400-44-400000000-22-22-22-220000004-400-22-22-22-22-22-22-22-22000000000000000000000000
χ5344-4-40040000-4400-44-4000000002-22-2-22-22000000-44002-22-2-22-222-22-2-22-22000000000000000000000000
χ5444-4-40040000-4400-44-400000000-22-222-22-2000000-4400-22-222-22-2-22-222-22-2000000000000000000000000
χ5544-4-400-200004-4002-2223−2323−2300002-22-22-22-2000023−23-2200−1+31−3−1+31−3−1−31+3−1−31+3−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000
χ5644-4-400-200004-4002-2223−2323−230000-22-22-22-22000023−23-22001−3−1+31−3−1+31+3−1−31+3−1−31+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000
χ5744-4-400-200004-4002-22−2323−232300002-22-22-22-20000−2323-2200−1−31+3−1−31+3−1+31−3−1+31−3−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000
χ5844-4-400-200004-4002-22−2323−23230000-22-22-22-220000−2323-22001+3−1−31+3−1−31−3−1+31−3−1+31−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000
χ5944-4-400-20000-44002-2223−2323−2300002-22-2-22-220000−23232-200−1+31−3−1+31−31+3−1−31+3−1−3−1−31+3−1−31+31−3−1+31−3−1+3000000000000000000000000
χ6044-4-400-20000-44002-2223−2323−230000-22-222-22-20000−23232-2001−3−1+31−3−1+3−1−31+3−1−31+31+3−1−31+3−1−3−1+31−3−1+31−3000000000000000000000000
χ6144-4-400-20000-44002-22−2323−232300002-22-2-22-22000023−232-200−1−31+3−1−31+31−3−1+31−3−1+3−1+31−3−1+31−31+3−1−31+3−1−3000000000000000000000000
χ6244-4-400-20000-44002-22−2323−23230000-22-222-22-2000023−232-2001+3−1−31+3−1−3−1+31−3−1+31−31−3−1+31−3−1+3−1−31+3−1−31+3000000000000000000000000
χ634-44-40044-4000000-4-4400000000000022−22−2222004-4000000000022−22−2222000022−22−2222000000000000000000000000
χ644-44-40044-4000000-4-44000000000000−222222−22004-40000000000−222222−220000−222222−22000000000000000000000000
χ654-44-4004-44000000-4-440000000022−22−2222000000-4400000022−22−2222000022−22−22220000000000000000000000000000
χ664-44-4004-44000000-4-4400000000−222222−22000000-44000000−222222−220000−222222−220000000000000000000000000000
χ674-44-400-24-400000022-223−23−23230000000022−22−222200-22000023−2300002ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ2300002ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000
χ684-44-400-24-400000022-223−23−232300000000−222222−2200-22000023−230000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ230000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000
χ694-44-400-24-400000022-2−232323−230000000022−22−222200-220000−232300002ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ700002ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000
χ704-44-400-24-400000022-2−232323−2300000000−222222−2200-220000−23230000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ70000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000
χ714-44-400-2-4400000022-223−23−2323000022−22−22220000002-20000−23232ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ700002ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000
χ724-44-400-2-4400000022-223−23−23230000−222222−220000002-20000−2323−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ70000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000
χ734-44-400-2-4400000022-2−232323−23000022−22−22220000002-2000023−232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ2300002ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000
χ744-44-400-2-4400000022-2−232323−230000−222222−220000002-2000023−23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ230000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000
χ754-4-444-4400-4400-444-4-4-4-444004-400000000-44000000000000000000000000000000000000000000000000
χ764-4-444-4-2004-4004-4-222-2-22200-222222−22−222222−22−22-2200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ774-4-444-4-2004-4004-4-222-2-22200-22−22−222222−22−222222-220000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ784-4-444-4-200-4400-44-22222-2-200-22000000002-20000000066−6−666−6−6−6−666−6−666000000000000000000000000
χ794-4-444-4-200-4400-44-22222-2-200-22000000002-200000000−6−666−6−66666−6−666−6−6000000000000000000000000
χ804-4-44-44400-44004-44-4-4-4-44400-44000000004-4000000000000000000000000000000000000000000000000
χ814-4-44-44-2004-400-44-222-2-222002-22222−22−22−22−2222222-200000000−2−22222−2−2−2−22222−2−2000000000000000000000000
χ824-4-44-44-2004-400-44-222-2-222002-2−22−2222222222−22−222-20000000022−2−2−2−22222−2−2−2−222000000000000000000000000
χ834-4-44-44-200-44004-4-22222-2-2002-200000000-220000000066−6−6−6−666−6−66666−6−6000000000000000000000000
χ844-4-44-44-200-44004-4-22222-2-2002-200000000-2200000000−6−66666−6−666−6−6−6−666000000000000000000000000

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