Finite Group Databasebeta

← Group #13156518

Character table — Group #13156518

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
order1222333446666666661212121233366666666612121212121212121212121244448888121212121212121224242424242424243666121212121212121212121212121212121212242424242424242424242424888824242424242424244121212121212121244121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200002222-2-2-2-2000000002222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2-2-22222000000002222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000
χ11222222-1222222-1-122-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000222-1-1-1-1-1-12000-1-10
χ12222222-1222222-1-122-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2111111-2000110
χ13222222-1222222-1-122-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000222-1-1-1-1-1-1-2000110
χ14222222-1222222-1-122-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-2-2-21111112000-1-10
χ15222222-1-2-22222-1-122-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-11111000000000000000000000000000−i3i3−i3−i3i3i30000−i3i30
χ16222222-1-2-22222-1-122-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-11111000000000000000000000000000i3−i3i3i3−i3−i30000i3−i30
χ17222222-1-2-22222-1-122-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-1000000000000000000000000000−i3i3−i3−i3i3i30000i3−i30
χ18222222-1-2-22222-1-122-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-1000000000000000000000000000i3−i3i3i3−i3−i30000−i3i30
χ1922222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111110000000000000000
χ2122222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2222222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ2322222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-21122-2-20000-1-1-1-111113333−3−3−3−3-1-1-1-1-2-2111122-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−30000000000000000
χ2422222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-21122-2-20000-1-1-1-11111−3−3−3−33333-1-1-1-1-2-2111122-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−333330000000000000000
χ2522222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211-2-22200001111-1-1-1-13333−3−3−3−3-1-1-1-1-2-21111-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−333330000000000000000
χ2622222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211-2-22200001111-1-1-1-1−3−3−3−33333-1-1-1-1-2-21111-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−30000000000000000
χ272222-12222-122222-1-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-122-1-1-1-102-1-1000
χ282222-12222-122222-1-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-211-2-211110-211000
χ292222-12222-122222-1-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000000000001111111111110000000000002-1-122-1-1-1-10-211000
χ302222-12222-122222-1-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-211-2-2111102-1-1000
χ3122-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-20000000000002-20022−2−222-2-2000022−2−222−2−222-2-20000002-20022-2-2000022−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ3222-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-20000000000002-200−2−22222-2-20000−2−222−2−22222-2-20000002-20022-2-20000−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ3322-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-2000000000000-220022−2−2-2-222000022−2−222−2−222-2-2000000-2200-2-222000022−2−222−2−222−2−2−2−222−2−222−2−2220000000000000000
χ3422-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-2000000000000-2200−2−222-2-2220000−2−222−2−22222-2-2000000-2200-2-2220000−2−222−2−222−2−22222−2−222−2−222−2−20000000000000000
χ3522-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−32-20022−2−2-1-11133−3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-1110033−3−32-200-1-11133−3−322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230000000000000000
χ3622-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−32-200−2−222-1-11133−3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-1110033−3−32-200-1-11133−3−3−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230000000000000000
χ3722-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−3-220022−2−211-1-1−3−333ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-1110033−3−3-220011-1-1−3−33322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230000000000000000
χ3822-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−3-2200−2−22211-1-1−3−333−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-1110033−3−3-220011-1-1−3−333−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230000000000000000
χ3922-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−332-20022−2−2-1-111−3−333ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-1-11100−3−3332-200-1-111−3−33322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70000000000000000
χ4022-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−332-200−2−222-1-111−3−333−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-1-11100−3−3332-200-1-111−3−333−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000
χ4122-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−33-220022−2−211-1-133−3−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-1-11100−3−333-220011-1-133−3−322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000
χ4222-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−33-2200−2−22211-1-133−3−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-1-11100−3−333-220011-1-133−3−3−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70000000000000000
χ432-22-22222-2-22-2-2-2-22-2222-2-2222-2-2-2-222-2-22-22-2-2-22-22-22220000000000000000000000002-2-222-22-22-20000000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ442-22-22222-2-22-2-2-2-22-2222-2-2222-2-2-2-222-2-22-22-2-2-22-22-22220000000000000000000000002-2-222-22-22-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ452-22-2222-22-22-2-2-2-22-22-2-222222-2-2-2-222-2-222-2222-22-22-2-2-200002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-2-22-22-22-220000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ462-22-2222-22-22-2-2-2-22-22-2-222222-2-2-2-222-2-222-2222-22-22-2-2-20000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-2-22-22-22-22000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ472-22-22-122-2-2-111-2-22-22-1-111-12-111-2-2-1-1112-22-211-11-112-1-1000000003−33−33−33−3−i3i3−i3i3i3−i3i3−i3-111-12-2-11-1100003−33−33−33−30000−i3i3−i3i3i3−i3i3−i32i−2i2i−2i−ii−ii−ii−ii0000000000000000
χ482-22-22-122-2-2-111-2-22-22-1-111-12-111-2-2-1-1112-22-211-11-112-1-1000000003−33−33−33−3i3−i3i3−i3−i3i3−i3i3-111-12-2-11-1100003−33−33−33−30000i3−i3i3−i3−i3i3−i3i3−2i2i−2i2ii−ii−ii−ii−i0000000000000000
χ492-22-22-122-2-2-111-2-22-22-1-111-12-111-2-2-1-1112-22-211-11-112-1-100000000−33−33−33−33−i3i3−i3i3i3−i3i3−i3-111-12-2-11-110000−33−33−33−330000−i3i3−i3i3i3−i3i3−i3−2i2i−2i2ii−ii−ii−ii−i0000000000000000
χ502-22-22-122-2-2-111-2-22-22-1-111-12-111-2-2-1-1112-22-211-11-112-1-100000000−33−33−33−33i3−i3i3−i3−i3i3−i3i3-111-12-2-11-110000−33−33−33−330000i3−i3i3−i3−i3i3−i3i32i−2i2i−2i−ii−ii−ii−ii0000000000000000
χ512-22-22-12-22-2-111-2-22-2211-1-1-12-111-2-2-1-11122-22-1-11-11-1-21100002i−2i2i−2i3−33−3−33−33−ii−ii−ii−ii-111-1-221-11-100003−33−3−33−332i−2i2i−2i−ii−ii−ii−ii0000i3−i3i3−i3−i3i3−i3i30000000000000000
χ522-22-22-12-22-2-111-2-22-2211-1-1-12-111-2-2-1-11122-22-1-11-11-1-21100002i−2i2i−2i−33−333−33−3−ii−ii−ii−ii-111-1-221-11-10000−33−333−33−32i−2i2i−2i−ii−ii−ii−ii0000−i3i3−i3i3i3−i3i3−i30000000000000000
χ532-22-22-12-22-2-111-2-22-2211-1-1-12-111-2-2-1-11122-22-1-11-11-1-2110000−2i2i−2i2i3−33−3−33−33i−ii−ii−ii−i-111-1-221-11-100003−33−3−33−33−2i2i−2i2ii−ii−ii−ii−i0000−i3i3−i3i3i3−i3i3−i30000000000000000
χ542-22-22-12-22-2-111-2-22-2211-1-1-12-111-2-2-1-11122-22-1-11-11-1-2110000−2i2i−2i2i−33−333−33−3i−ii−ii−ii−i-111-1-221-11-10000−33−333−33−3−2i2i−2i2ii−ii−ii−ii−i0000i3−i3i3−i3−i3i3−i3i30000000000000000
χ552-22-2-122-2212-2-2-2-2-112-2-222-1-121111-12-2-2-1-1-22-1-1-22-2211100002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i-111-11-11-11-1000000000000−ii−ii−ii−ii−ii−ii0000000000000−i3i300−i3i3−i3i3003−3000
χ562-22-2-122-2212-2-2-2-2-112-2-222-1-121111-12-2-2-1-1-22-1-1-22-2211100002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i-111-11-11-11-1000000000000−ii−ii−ii−ii−ii−ii0000000000000i3−i300i3−i3i3−i300−33000
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χ1248888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-2000000000000000000000000-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000
χ12588-8-8-48-400-4-88-8-444440000-42-4-442-244-44-200000000000000000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ12688-8-8-4-4-400-44-44-4444443−4343−432222-22-2-2-22-2-2000−2323−23−2323230−2323000000000000000000000000-1-1110033−3−30000000000000000000000000000000000000000000000000000
χ12788-8-8-4-4-400-44-44-44444−4343−43432222-22-2-2-22-2-200023−232323−23−23023−23000000000000000000000000-1-11100−3−3330000000000000000000000000000000000000000000000000000
χ1288-88-8-4-4-48-84-44444-44-4-4-444222-2-2-2-222-2-224-44-2-22-22-2-422000000000000000000000000-111-12-2-11-110000000000000000000000000000000000000000000000000000
χ1298-88-8-4-4-4-884-44444-44-444-4-4222-2-2-2-222-2-22-44-422-22-224-2-2000000000000000000000000-111-1-221-11-10000000000000000000000000000000000000000000000000000
χ1308-8-88-48-4004-8-884-44-440000-42-44-4-22444-4-20000000000000000000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1318-8-88-4-4-400444-44-44-4443−43−4343222-22-22-2-2-22-200023−23−232323−230−2323000000000000000000000000-11-11003−3−330000000000000000000000000000000000000000000000000000
χ1328-8-88-4-4-400444-44-44-44−434343−43222-22-22-2-2-22-2000−232323−23−2323023−23000000000000000000000000-11-1100−333−30000000000000000000000000000000000000000000000000000

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