Finite Group Databasebeta

← Group #13156004

Character table — Group #13156004

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order122233344666666666121212123336666666661212121212121212121212124412121212366612121212121244488121212121212121212121212121212121212242424242424242424242424242424241212121212122266668824242424412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2000022-2-2-2-200002222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-220000-2-222220000-2-2-2-2222200000000000000000000000000000000000000
χ11222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-122-1-1-1-10000000000
χ12222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2002222-1-11111-1-1-1-1-1-1-1-10000000000000000-2-21111-2-211110000000000
χ13222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-22200-2-2-2-211-1-1-1-111111111000000000000000022-1-1-1-1-2-211110000000000
χ14222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-200-2-2-2-2111111111111110000000000000000-2-2111122-1-1-1-10000000000
χ15222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-2000022-2-211−i3−i3i3i3-1-1-1-11111000000000000000000−i3−i3i3i300−i3−i3i3i30000000000
χ16222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-2000022-2-211i3i3−i3−i3-1-1-1-11111000000000000000000i3i3−i3−i300i3i3−i3−i30000000000
χ17222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-2-21111-1-1-1-111111120000-2-222-1-1−i3−i3i3i31111-1-1-1-1000000000000000000−i3−i3i3i300i3i3−i3−i30000000000
χ18222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-2-21111-1-1-1-111111120000-2-222-1-1i3i3−i3−i31111-1-1-1-1000000000000000000i3i3−i3−i300−i3−i3i3i30000000000
χ1922222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-120022-1-1-1-1220000-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ2022222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-2-2-1-1-1-1220000-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000000-2-211110000
χ2122222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-200221111-2-2000011111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-2-211110000
χ2222222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-200-2-21111-2-20000111111111111-2-2-2-21111111100000000000022-1-1-1-10000
χ2322222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211222222-1-1-1-1-2-21111-20000-1-111-2-20000-1-1-1-1111133−3−300003333−3−3−3−30000000000000033−3−30000
χ2422222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211222222-1-1-1-1-2-21111-20000-1-111-2-20000-1-1-1-11111−3−3330000−3−3−3−3333300000000000000−3−3330000
χ2522222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-211112000011-1-12200001111-1-1-1-133−3−300003333−3−3−3−300000000000000−3−3330000
χ2622222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-211112000011-1-12200001111-1-1-1-1−3−3330000−3−3−3−333330000000000000033−3−30000
χ272222-12222-122222-12-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022220000002222000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ282222-12222-122222-12-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022-2-2000000222200000000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ292222-12222-122222-12-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-222000000-2-2-2-2000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ302222-12222-122222-12-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-2-2-2000000-2-2-2-200000000-2-2-2-21111111111111111110000000000002-1-10
χ312-22-222200-2-2-22-2-222-200002222-2-2-2-2-22-220000000000002-222-2-222-2-2000000000−i2i22-20000000022-2-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i20000
χ322-22-222200-2-2-22-2-222-200002222-2-2-2-2-22-220000000000002-222-2-222-2-2000000000i2−i22-20000000022-2-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i20000
χ332-22-222200-2-2-22-2-222-200002222-2-2-2-2-22-22000000000000-22-2-22222-2-2000000000−i2i2-2200000000-2-2220000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i20000
χ342-22-222200-2-2-22-2-222-200002222-2-2-2-2-22-22000000000000-22-2-22222-2-2000000000i2−i2-2200000000-2-2220000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i20000
χ352-22-22-1200-21-2-11-222-23−33−3-12-1-11-21-21-1120003−333−3−303−32-222-2-2-1-1110033−3−3000−i2i2-113−3000000-1-11133−3−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ362-22-22-1200-21-2-11-222-23−33−3-12-1-11-21-21-1120003−333−3−303−32-222-2-2-1-1110033−3−3000i2−i2-113−3000000-1-11133−3−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ372-22-22-1200-21-2-11-222-23−33−3-12-1-11-21-21-1120003−333−3−303−3-22-2-222-1-1110033−3−3000−i2i21-1−3300000011-1-1−3−333ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ382-22-22-1200-21-2-11-222-23−33−3-12-1-11-21-21-1120003−333−3−303−3-22-2-222-1-1110033−3−3000i2−i21-1−3300000011-1-1−3−333−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ392-22-22-1200-21-2-11-222-2−33−33-12-1-11-21-21-112000−33−3−3330−332-222-2-2-1-11100−3−333000−i2i2-11−33000000-1-111−3−333ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ402-22-22-1200-21-2-11-222-2−33−33-12-1-11-21-21-112000−33−3−3330−332-222-2-2-1-11100−3−333000i2−i2-11−33000000-1-111−3−333−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ412-22-22-1200-21-2-11-222-2−33−33-12-1-11-21-21-112000−33−3−3330−33-22-2-222-1-11100−3−333000−i2i21-13−300000011-1-133−3−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ422-22-22-1200-21-2-11-222-2−33−33-12-1-11-21-21-112000−33−3−3330−33-22-2-222-1-11100−3−333000i2−i21-13−300000011-1-133−3−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ432-2-222222-2-222-2-2-2-2-2222-2-2222-2-2-2222-2-2-22-22222-22-2-2-2-20000002-2-222-22-22-202i−2i000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i2i−2i0000000000000000
χ442-2-222222-2-222-2-2-2-2-2222-2-2222-2-2-2222-2-2-22-22222-22-2-2-2-20000002-2-222-22-22-20−2i2i00000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i−2i2i0000000000000000
χ452-2-22222-22-222-2-2-2-2-22-2-222222-2-2-2222-2-2-2-22-2-2-2-22-222220000002-2-22-22-22-220000000000000000000000000000000000000000000002-22-22-20000000000
χ462-2-22222-22-222-2-2-2-2-22-2-222222-2-2-2222-2-2-2-22-2-2-2-22-222220000002-2-22-22-22-22000000000000000000000000000000000000000000000-22-22-220000000000
χ472-2-2222-12-2-22-1-2-21-21222-2-22-1-1-2-212-1-1111-11222-11-11-2-2-2003−33−3-111-1-11-11-1102i−2i0000003−3−ii−ii3−33−33−33−300000000000000002i−2i−ii−ii00−i3i3i3−i30000000000
χ482-2-2222-12-2-22-1-2-21-21222-2-22-1-1-2-212-1-1111-11222-11-11-2-2-2003−33−3-111-1-11-11-110−2i2i0000003−3i−ii−i3−33−33−33−30000000000000000−2i2ii−ii−i00i3−i3−i3i30000000000
χ492-2-2222-12-2-22-1-2-21-21222-2-22-1-1-2-212-1-1111-11222-11-11-2-2-200−33−33-111-1-11-11-1102i−2i000000−33−ii−ii−33−33−33−3300000000000000002i−2i−ii−ii00i3−i3−i3i30000000000
χ502-2-2222-12-2-22-1-2-21-21222-2-22-1-1-2-212-1-1111-11222-11-11-2-2-200−33−33-111-1-11-11-110−2i2i000000−33i−ii−i−33−33−33−330000000000000000−2i2ii−ii−i00−i3i3i3−i30000000000
χ512-2-2222-1-22-22-1-2-21-212-2-2222-1-1-2-212-1-11111-1-2-2-21-11-1222003−33−3-111-11-11-11-1000000000−333−3−333−33−3−33−330000000000000000003−3−332-2-11-110000000000
χ522-2-2222-1-22-22-1-2-21-212-2-2222-1-1-2-212-1-11111-1-2-2-21-11-1222003−33−3-111-11-11-11-1000000000−33−333−33−33−3−33−33000000000000000000−333−3-221-11-10000000000
χ532-2-2222-1-22-22-1-2-21-212-2-2222-1-1-2-212-1-11111-1-2-2-21-11-122200−33−33-111-11-11-11-10000000003−33−3−33−33−333−33−30000000000000000003−3−33-221-11-10000000000
χ542-2-2222-1-22-22-1-2-21-212-2-2222-1-1-2-212-1-11111-1-2-2-21-11-122200−33−33-111-11-11-11-10000000003−3−333−3−33−333−33−3000000000000000000−333−32-2-11-110000000000
χ552-2-22-1222-2122-2-2-21-2-122-2-2-1-12111-1-12-2-212-2-1-1-12-22-2111000000-111-1-11-11-1102i−2i000000002i−2i2i−2i0000000000003−33−33−33−33−33−3−ii−ii−ii0000000000000−i3i30
χ562-2-22-1222-2122-2-2-21-2-122-2-2-1-12111-1-12-2-212-2-1-1-12-22-2111000000-111-1-11-11-1102i−2i000000002i−2i2i−2i000000000000−33−33−33−33−33−33−ii−ii−ii0000000000000i3−i30
χ572-2-22-1222-2122-2-2-21-2-122-2-2-1-12111-1-12-2-212-2-1-1-12-22-2111000000-111-1-11-11-110−2i2i00000000−2i2i−2i2i0000000000003−33−33−33−33−33−3i−ii−ii−i0000000000000i3−i30
χ582-2-22-1222-2122-2-2-21-2-122-2-2-1-12111-1-12-2-212-2-1-1-12-22-2111000000-111-1-11-11-110−2i2i00000000−2i2i−2i2i000000000000−33−33−33−33−33−33i−ii−ii−i0000000000000−i3i30
χ5944444-2-2444-2-2-2-2-24-24-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-244-2-2-2-21111-2-2111140000-2-2-2-2-2-200001111111100000000000000000000000000000000000000
χ6044444-2-2444-2-2-2-2-24-24-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-2-4-422221111-2-21111-400002222220000-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ6144444-2-2-4-44-2-2-2-2-24-242222-2-21-2-2-2-2-2111-222-422-1-1-1-1-42244-2-2-2-2111122-1-1-1-1-40000-2-2222200001111-1-1-1-100000000000000000000000000000000000000
χ6244444-2-2-4-44-2-2-2-2-24-242222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422-4-42222111122-1-1-1-14000022-2-2-2-20000-1-1-1-1111100000000000000000000000000000000000000
χ634444-244-4-4-244444-24-2-4-4-4-4-2-24-2-2-2-2-2444-2-4-4222-4-4-4-4222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ644444-24-244-24-244-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2000000111111111104400000000-2-2-2-2000000000000000000000000-2-211110000000000000000
χ654444-24-244-24-244-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-200000011111111110-4-400000000222200000000000000000000000022-1-1-1-10000000000000000
χ664444-24-2-4-4-24-244-2-2-2-2-4-4-4-4-21-2-2-21-21-2-2-212222222222220000001111-1-1-1-1-1-100000000000−2i3−2i32i32i300000000000000000000000000i3i3−i3−i30000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.