Finite Group Databasebeta

← Group #13156040

Character table — Group #13156040

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order1222333446666666661212121233366666666612121212121212121212121244121212123666121212121212224666688121212121212121212121212121224242424242424242424242424242424666666448812121212242424242664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200-200000022-2-2-2-22222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2002000000-2-22222-2-2-2-2222200000000000000000000000000000000000000
χ11222222-122-1-122-1222222222-1-1-1-1-1-12-1-12222-12222-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1220222222000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ12222222-122-1-122-1222222222-1-1-1-1-1-12-1-12222-12222-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-12202222-2-200000000000000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ13222222-122-1-122-1222222222-1-1-1-1-1-12-1-12222-12222-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-222000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ14222222-122-1-122-1222222222-1-1-1-1-1-12-1-12222-12222-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-200000000000000-2-2-2-21111111111111111110000000000002-1-10
χ1522222-1222222-1222-1-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ1622222-1222222-1222-1-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-221111002222-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111-2-200111100000000
χ1722222-1222222-1222-1-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-122222-2-21111-1-1-1-1-1-1-1-1-1-122-2-1-1-1-100-2-2-2-21111111111000000000000000022-1-1-1-1-2-200111100000000
χ1822222-1222222-1222-1-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-122222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2111100-2-2-2-211111111110000000000000000-2-211112200-1-1-1-100000000
χ1922222-12-2-2222-1222-1-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-222-1-1-1-1-1-1-1-111111100-2−i3−i3i3i30022-2-211-1-1-1-11111000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ2022222-12-2-2222-1222-1-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-222-1-1-1-1-1-1-1-111111100-2i3i3−i3−i30022-2-211-1-1-1-11111000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ2122222-12-2-2222-1222-1-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-2-2-21111-1-1-1-1111111002−i3−i3i3i300-2-222-1-11111-1-1-1-1000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ2222222-12-2-2222-1222-1-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-2-2-21111-1-1-1-1111111002i3i3−i3−i300-2-222-1-11111-1-1-1-1000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ232222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1002000022-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ242222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-10020000-2-2-1-1-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ252222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-100-20000221111-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ262222-1222222-122-1-122-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-100-20000-2-21111-2-2111111111111-2-2-2-21111111100000000220000-1-1-1-10000
χ272222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-211222222-1-1-1-1-2-2111100-2000000-1-111-2-2-1-1-1-1111133−3−300003333−3−3−3−30000000000000033−3−30000
χ282222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-211222222-1-1-1-1-2-2111100-2000000-1-111-2-2-1-1-1-11111−3−3330000−3−3−3−3333300000000000000−3−3330000
χ292222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-2111100200000011-1-1221111-1-1-1-133−3−300003333−3−3−3−300000000000000−3−3330000
χ302222-122-2-222-122-1-1221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-2111100200000011-1-1221111-1-1-1-1−3−3330000−3−3−3−333330000000000000033−3−30000
χ3122-2-2222002-2-2-2-22-22-200002222-22-2-2-2-22-20000000000002i−2i2i2i−2i−2i22-2-200000000000002−22i−2i00002i2i−2i−2i00002−22−222−2−222−2−222−2−200000000−i2i20000−i2i2−i2i20000
χ3222-2-2222002-2-2-2-22-22-200002222-22-2-2-2-22-20000000000002i−2i2i2i−2i−2i22-2-20000000000000−222i−2i00002i2i−2i−2i0000−22−22−2−222−2−222−2−22200000000i2−i20000i2−i2i2−i20000
χ3322-2-2222002-2-2-2-22-22-200002222-22-2-2-2-22-2000000000000−2i2i−2i−2i2i2i22-2-200000000000002−2−2i2i0000−2i−2i2i2i00002−22−222−2−222−2−222−2−200000000i2−i20000i2−i2i2−i20000
χ3422-2-2222002-2-2-2-22-22-200002222-22-2-2-2-22-2000000000000−2i2i−2i−2i2i2i22-2-20000000000000−22−2i2i0000−2i−2i2i2i0000−22−22−2−222−2−222−2−22200000000−i2i20000−i2i2−i2i20000
χ3522-2-2-122002-21-2-2-112-23−33−3-1-12-112-211-2-1100033−3−33−303−32i−2i2i2i−2i−2i-1-1110033−3−300000002−2−ii−i3i300−i−iii−i3−i3i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ3622-2-2-122002-21-2-2-112-23−33−3-1-12-112-211-2-1100033−3−33−303−32i−2i2i2i−2i−2i-1-1110033−3−30000000−22−ii−i3i300−i−iii−i3−i3i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ3722-2-2-122002-21-2-2-112-23−33−3-1-12-112-211-2-1100033−3−33−303−3−2i2i−2i−2i2i2i-1-1110033−3−300000002−2i−ii3−i300ii−i−ii3i3−i3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ3822-2-2-122002-21-2-2-112-23−33−3-1-12-112-211-2-1100033−3−33−303−3−2i2i−2i−2i2i2i-1-1110033−3−30000000−22i−ii3−i300ii−i−ii3i3−i3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ3922-2-2-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−3−333−330−332i−2i2i2i−2i−2i-1-11100−3−33300000002−2−iii3−i300−i−iiii3i3−i3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ4022-2-2-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−3−333−330−332i−2i2i2i−2i−2i-1-11100−3−3330000000−22−iii3−i300−i−iiii3i3−i3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ4122-2-2-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−3−333−330−33−2i2i−2i−2i2i2i-1-11100−3−33300000002−2i−i−i3i300ii−i−i−i3−i3i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ4222-2-2-122002-21-2-2-112-2−33−33-1-12-112-211-2-11000−3−333−330−33−2i2i−2i−2i2i2i-1-11100−3−3330000000−22i−i−i3i300ii−i−i−i3−i3i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ432-2-222222-2-2-2222-2-2-2-222-2-2222-2-2-2-2222-2-22-222-22-222-2-2-20000002-2-222-22-22-20000000000000000000000000000000000000000000002i−2i002i−2i2i−2i00000000
χ442-2-222222-2-2-2222-2-2-2-222-2-2222-2-2-2-2222-2-22-222-22-222-2-2-20000002-2-222-22-22-2000000000000000000000000000000000000000000000−2i2i00−2i2i−2i2i00000000
χ452-2-22222-22-2-2222-2-2-2-2-2-222222-2-2-2-2222-2-2-22-2-22-22-2-22220000002-2-22-22-22-222-202-22-2000000000000000000000000000000002-22-22-20000000000000000
χ462-2-22222-22-2-2222-2-2-2-2-2-222222-2-2-2-2222-2-2-22-2-22-22-2-22220000002-2-22-22-22-22-220-22-2200000000000000000000000000000000-22-22-220000000000000000
χ472-2-2222-1-221122-1-2-2-2-2-2-2222-1-111112-1-1-2-2-221-22-2211-1-1-1000000-111-11-11-11-12-202-22-200000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-11-11-110000000000000−i3i30
χ482-2-2222-1-221122-1-2-2-2-2-2-2222-1-111112-1-1-2-2-221-22-2211-1-1-1000000-111-11-11-11-12-202-22-200000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-11-11-110000000000000i3−i30
χ492-2-2222-1-221122-1-2-2-2-2-2-2222-1-111112-1-1-2-2-221-22-2211-1-1-1000000-111-11-11-11-1-220-22-2200000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i31-11-11-10000000000000i3−i30
χ502-2-2222-1-221122-1-2-2-2-2-2-2222-1-111112-1-1-2-2-221-22-2211-1-1-1000000-111-11-11-11-1-220-22-2200000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i31-11-11-10000000000000−i3i30
χ512-2-222-122-2-2-22-12-2-21122-2-2-12-1-2-211-12-111-112-11-1122-2-2-2003−33−3-111-1-11-11-11000−i3i3i3−i30000003−33−33−33−33−3000000000000000000−i3i3i3−i32i−2i00−ii−ii00000000
χ522-2-222-122-2-2-22-12-2-21122-2-2-12-1-2-211-12-111-112-11-1122-2-2-2003−33−3-111-1-11-11-11000i3−i3−i3i30000003−33−33−33−33−3000000000000000000i3−i3−i3i3−2i2i00i−ii−i00000000
χ532-2-222-122-2-2-22-12-2-21122-2-2-12-1-2-211-12-111-112-11-1122-2-2-200−33−33-111-1-11-11-11000−i3i3i3−i3000000−33−33−33−33−33000000000000000000−i3i3i3−i3−2i2i00i−ii−i00000000
χ542-2-222-122-2-2-22-12-2-21122-2-2-12-1-2-211-12-111-112-11-1122-2-2-200−33−33-111-1-11-11-11000i3−i3−i3i3000000−33−33−33−33−33000000000000000000i3−i3−i3i32i−2i00−ii−ii00000000
χ552-2-222-12-22-2-22-12-2-211-2-222-12-1-2-211-12-1111-1-21-11-1-2-2222003−33−3-111-11-11-11-12-20-11-11000000−333−33−3−33−3300000000000000002-2-11-1100003−3−3300000000
χ562-2-222-12-22-2-22-12-2-211-2-222-12-1-2-211-12-1111-1-21-11-1-2-2222003−33−3-111-11-11-11-1-2201-11-1000000−333−33−3−33−330000000000000000-221-11-10000−333−300000000
χ572-2-222-12-22-2-22-12-2-211-2-222-12-1-2-211-12-1111-1-21-11-1-2-222200−33−33-111-11-11-11-12-20-11-110000003−3−33−333−33−300000000000000002-2-11-110000−333−300000000
χ582-2-222-12-22-2-22-12-2-211-2-222-12-1-2-211-12-1111-1-21-11-1-2-222200−33−33-111-11-11-11-1-2201-11-10000003−3−33−333−33−30000000000000000-221-11-100003−3−3300000000
χ59444444-2-4-4-2-244-24444-4-4-4-44-2-2-2-2-2-24-2-244-4-42-4-4-4-422222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ6044444-2-244-2-24-2-244-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-20000001111111111440-2-2-2-200000000000000000000000000000000-2-211110000000000000000
χ6144444-2-244-2-24-2-244-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-20000001111111111-4-4022220000000000000000000000000000000022-1-1-1-10000000000000000
χ6244444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-211-2-21-2-22222222222220000001111-1-1-1-1-1-1000−2i3−2i32i32i30000000000000000000000000000000000i3i3−i3−i30000000000000000
χ6344444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-211-2-21-2-22222222222220000001111-1-1-1-1-1-10002i32i3−2i3−2i30000000000000000000000000000000000−i3−i3i3i30000000000000000
χ644444-24-244-2-2-24-2-2-244-2-2-2-2-21-211-2-2-21-2-2-244-2-2-2-2-211-2110000001111-2-2111100000004400000000000000-2-2-2-2-2-2-2-2111111110000000000000000000000
χ654444-24-244-2-2-24-2-2-244-2-2-2-2-21-211-2-2-21-2-2-244-2-2-2-2-211-2110000001111-2-211110000000-4-40000000000000022222222-1-1-1-1-1-1-1-10000000000000000000000
χ664444-24-2-4-4-2-2-24-2-2-2442222-21-211-2-2-21-2-2-2-4-422222-1-12-1-1000000111122-1-1-1-1000000000000000000000002323−23−230000−3−3−3−333330000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.