Finite Group Databasebeta

← Group #13156365

Character table — Group #13156365

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order1222333446666666661212121233366666666612121212121212121212121244121212123666121212121212444881212121212121212121212121212121212122424242424242424242424242424242412121212121244881212121224242424412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
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
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11
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
χ11222222-12222222-1-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ12222222-12222222-1-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2002222-1-11111-1-1-1-1-1-1-1-10000000000000000-2-21111-2-200111100000000
χ13222222-12222222-1-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-22200-2-2-2-211-1-1-1-111111111000000000000000022-1-1-1-1-2-200111100000000
χ14222222-12222222-1-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-200-2-2-2-2111111111111110000000000000000-2-211112200-1-1-1-100000000
χ15222222-1-2-222222-1-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-2000022-2-211−i3−i3i3i3-1-1-1-11111000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ16222222-1-2-222222-1-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-2000022-2-211i3i3−i3−i3-1-1-1-11111000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ17222222-1-2-222222-1-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120000-2-222-1-1−i3−i3i3i31111-1-1-1-1000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ18222222-1-2-222222-1-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120000-2-222-1-1i3i3−i3−i31111-1-1-1-1000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ1922222-122222-1-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-120022-1-1-1-1220000-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ2022222-122222-1-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-2-2-1-1-1-1220000-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ2122222-122222-1-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-200221111-2-2000011111111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ2222222-122222-1-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-200-2-21111-2-20000111111111111-2-2-2-21111111100000000220000-1-1-1-10000
χ2322222-12-2-222-1-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211222222-1-1-1-1-2-21111-20000-1-111-2-20000-1-1-1-1111133−3−300003333−3−3−3−30000000000000033−3−30000
χ2422222-12-2-222-1-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211222222-1-1-1-1-2-21111-20000-1-111-2-20000-1-1-1-11111−3−3330000−3−3−3−3333300000000000000−3−3330000
χ2522222-12-2-222-1-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-211112000011-1-12200001111-1-1-1-133−3−300003333−3−3−3−300000000000000−3−3330000
χ2622222-12-2-222-1-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-211112000011-1-12200001111-1-1-1-1−3−3330000−3−3−3−333330000000000000033−3−30000
χ272222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022220000002222000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ282222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022-2-2000000222200000000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ292222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-222000000-2-2-2-2000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ302222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-2-2-2000000-2-2-2-200000000-2-2-2-21111111111111111110000000000002-1-10
χ3122-2-22222-2-222-2-2-2-22-222-2-2222-2-2-2222-2-2-222-22222-2-2-2-2-20000002-2-222-222-2-20000000000000000000000000000000000000000000002-2002-22-200000000
χ3222-2-22222-2-222-2-2-2-22-222-2-2222-2-2-2222-2-2-222-22222-2-2-2-2-20000002-2-222-222-2-2000000000000000000000000000000000000000000000-2200-22-2200000000
χ3322-2-2222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-2-22-2-2-2-2222220000002-2-22-22-2-22202i−2i000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i2i−2i0000000000000000
χ3422-2-2222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-2-22-2-2-2-2222220000002-2-22-22-2-2220−2i2i00000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i−2i2i0000000000000000
χ3522-2-222-12-2-222-2-211-1-222-2-22-1-1-2-212-1-11112-1122-1-111-2-2-20033−3−3-111-1-11-1-1110000000003−33−3−3333−3−333−3−30000000000000000003−3−332-200-11-1100000000
χ3622-2-222-12-2-222-2-211-1-222-2-22-1-1-2-212-1-11112-1122-1-111-2-2-20033−3−3-111-1-11-1-1110000000003−3−333−333−3−333−3−3000000000000000000−333−3-22001-11-100000000
χ3722-2-222-12-2-222-2-211-1-222-2-22-1-1-2-212-1-11112-1122-1-111-2-2-200−3−333-111-1-11-1-111000000000−333−3−33−3−333−3−3330000000000000000003−3−33-22001-11-100000000
χ3822-2-222-12-2-222-2-211-1-222-2-22-1-1-2-212-1-11112-1122-1-111-2-2-200−3−333-111-1-11-1-111000000000−33−333−3−3−333−3−333000000000000000000−333−32-200-11-1100000000
χ3922-2-222-1-22-222-2-211-1-2-2-2222-1-1-2-212-1-1111-21-1-2-211-1-12220033−3−3-111-11-111-1-102i−2i000000−33−ii−ii33−3−3−3−33300000000000000002i−2i−ii−ii0000−i3i3i3−i300000000
χ4022-2-222-1-22-222-2-211-1-2-2-2222-1-1-2-212-1-1111-21-1-2-211-1-12220033−3−3-111-11-111-1-10−2i2i000000−33i−ii−i33−3−3−3−3330000000000000000−2i2ii−ii−i0000i3−i3−i3i300000000
χ4122-2-222-1-22-222-2-211-1-2-2-2222-1-1-2-212-1-1111-21-1-2-211-1-122200−3−333-111-11-111-1-102i−2i0000003−3−ii−ii−3−33333−3−300000000000000002i−2i−ii−ii0000i3−i3−i3i300000000
χ4222-2-222-1-22-222-2-211-1-2-2-2222-1-1-2-212-1-1111-21-1-2-211-1-122200−3−333-111-11-111-1-10−2i2i0000003−3i−ii−i−3−33333−3−30000000000000000−2i2ii−ii−i0000−i3i3i3−i300000000
χ4322-2-2-122-221-12-2-2-2-221-2-222-1-12111-1-12-2-211-2211-2-222-1-1-1000000-111-11-111-1-102i−2i000000002i−2i2i−2i000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−ii−ii−ii00000000000003−30
χ4422-2-2-122-221-12-2-2-2-221-2-222-1-12111-1-12-2-211-2211-2-222-1-1-1000000-111-11-111-1-102i−2i000000002i−2i2i−2i000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−ii−ii−ii0000000000000−330
χ4522-2-2-122-221-12-2-2-2-221-2-222-1-12111-1-12-2-211-2211-2-222-1-1-1000000-111-11-111-1-10−2i2i00000000−2i2i−2i2i000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i−ii−ii−i0000000000000−330
χ4622-2-2-122-221-12-2-2-2-221-2-222-1-12111-1-12-2-211-2211-2-222-1-1-1000000-111-11-111-1-10−2i2i00000000−2i2i−2i2i000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i−ii−ii−i00000000000003−30
χ472-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-220000000000002i−2i2i−2i2i−2i22-2-20000000002−22i−2i000000002i−2i2i−2i00002−22−22−22−22−22−22−22−200000000−i2i20000−i2i2−i2i20000
χ482-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-220000000000002i−2i2i−2i2i−2i22-2-2000000000−222i−2i000000002i−2i2i−2i0000−22−22−22−22−22−22−22−2200000000i2−i20000i2−i2i2−i20000
χ492-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-22000000000000−2i2i−2i2i−2i2i22-2-20000000002−2−2i2i00000000−2i2i−2i2i00002−22−22−22−22−22−22−22−200000000i2−i20000i2−i2i2−i20000
χ502-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-22000000000000−2i2i−2i2i−2i2i22-2-2000000000−22−2i2i00000000−2i2i−2i2i0000−22−22−22−22−22−22−22−2200000000−i2i20000−i2i2−i2i20000
χ512-22-22-1200-2-21-11-22-223−33−3-12-1-11-21-21-1120003−33−33−303−32i−2i2i−2i2i−2i-1-111003−33−30002−2−ii−i3i3000000−ii−ii−i3i3−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ522-22-22-1200-2-21-11-22-223−33−3-12-1-11-21-21-1120003−33−33−303−32i−2i2i−2i2i−2i-1-111003−33−3000−22−ii−i3i3000000−ii−ii−i3i3−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ532-22-22-1200-2-21-11-22-223−33−3-12-1-11-21-21-1120003−33−33−303−3−2i2i−2i2i−2i2i-1-111003−33−30002−2i−ii3−i3000000i−ii−ii3−i3i3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ542-22-22-1200-2-21-11-22-223−33−3-12-1-11-21-21-1120003−33−33−303−3−2i2i−2i2i−2i2i-1-111003−33−3000−22i−ii3−i3000000i−ii−ii3−i3i3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ552-22-22-1200-2-21-11-22-22−33−33-12-1-11-21-21-112000−33−33−330−332i−2i2i−2i2i−2i-1-11100−33−330002−2−iii3−i3000000−ii−iii3−i3i3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ562-22-22-1200-2-21-11-22-22−33−33-12-1-11-21-21-112000−33−33−330−332i−2i2i−2i2i−2i-1-11100−33−33000−22−iii3−i3000000−ii−iii3−i3i3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ572-22-22-1200-2-21-11-22-22−33−33-12-1-11-21-21-112000−33−33−330−33−2i2i−2i2i−2i2i-1-11100−33−330002−2i−i−i3i3000000i−ii−i−i3i3−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ582-22-22-1200-2-21-11-22-22−33−33-12-1-11-21-21-112000−33−33−330−33−2i2i−2i2i−2i2i-1-11100−33−33000−22i−i−i3i3000000i−ii−i−i3i3−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ5944444-2-24444-2-2-2-2-2-24-2-2-2-2-2-21-2-2-2-2-2111-24-2-2-2-211114-2-244-2-2-2-21111-2-2111140000-2-2-2-2-2-200001111111100000000000000000000000000000000000000
χ6044444-2-24444-2-2-2-2-2-24-2-2-2-2-2-21-2-2-2-2-2111-24-2-2-2-211114-2-2-4-422221111-2-21111-400002222220000-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ6144444-2-2-4-444-2-2-2-2-2-242222-2-21-2-2-2-2-2111-2-42222-1-1-1-1-42244-2-2-2-2111122-1-1-1-1-40000-2-2222200001111-1-1-1-100000000000000000000000000000000000000
χ6244444-2-2-4-444-2-2-2-2-2-242222-2-21-2-2-2-2-2111-2-42222-1-1-1-1-422-4-42222111122-1-1-1-14000022-2-2-2-20000-1-1-1-1111100000000000000000000000000000000000000
χ634444-244-4-4-2-2444444-2-4-4-4-4-2-24-2-2-2-2-2444-22-4-422-4-4-4-4222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ644444-24-244-2-2444-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2000000111111111104400000000-2-2-2-2000000000000000000000000-2-211110000000000000000
χ654444-24-244-2-2444-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-200000011111111110-4-400000000222200000000000000000000000022-1-1-1-10000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.