Finite Group Databasebeta

← Group #13156318

Character table — Group #13156318

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
χ311111111111111111111111111111111111111111111111111111111111111-1-11111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200-20022-2-20000-2-22222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200200-2-222000022-2-2-2-2222200000000000000000000000000000000000000
χ11222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ12222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-220022221111-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111-2-200111100000000
χ13222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-122-200-2-2-2-2-1-1-1-11111111111000000000000000022-1-1-1-1-2-200111100000000
χ14222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-200-2-2-2-2111111111111110000000000000000-2-211112200-1-1-1-100000000
χ15222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-111111100-20022-2-2−i3−i3i3i311-1-1-1-11111000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ16222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-111111100-20022-2-2i3i3−i3−i311-1-1-1-11111000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ17222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111100200-2-222−i3−i3i3i3-1-11111-1-1-1-1000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ18222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111100200-2-222i3i3−i3−i3-1-11111-1-1-1-1000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ1922222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-100222-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ2022222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1002-2-2-1-1-1-1000022-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ2122222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-100-22211110000-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ2222222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2-2-211110000-2-2111111111111-2-2-2-21111111100000000220000-1-1-1-10000
χ2322222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211222222-1-1-1-1-2-2111100-200-1-1110000-2-2-1-1-1-1111133−3−300003333−3−3−3−30000000000000033−3−30000
χ2422222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211222222-1-1-1-1-2-2111100-200-1-1110000-2-2-1-1-1-11111−3−3330000−3−3−3−3333300000000000000−3−3330000
χ2522222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-211110020011-1-10000221111-1-1-1-133−3−300003333−3−3−3−300000000000000−3−3330000
χ2622222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-211110020011-1-10000221111-1-1-1-1−3−3330000−3−3−3−333330000000000000033−3−30000
χ272222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1220220000222200000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ282222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1220-2-2000022220000000000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ292222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1-2-20220000-2-2-2-200000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ302222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1-2-20-2-20000-2-2-2-20000000000-2-2-2-21111111111111111110000000000002-1-10
χ3122-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-20000000000002-222-2-222-2-20000000002−22-20000000022-2-200002−22−222−2−222−2−222−2−2000000002−200002−22−20000
χ3222-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-20000000000002-222-2-222-2-2000000000−222-20000000022-2-20000−22−22−2−222−2−222−2−22200000000−220000−22−220000
χ3322-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-2000000000000-22-2-22222-2-20000000002−2-2200000000-2-22200002−22−222−2−222−2−222−2−200000000−220000−22−220000
χ3422-2-2222002-22-22-2-2-2-200002222-22-2-2-22-2-2000000000000-22-2-22222-2-2000000000−22-2200000000-2-2220000−22−22−2−222−2−222−2−222000000002−200002−22−20000
χ3522-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−32-222-2-2-1-1110033−3−30002−2-113−3000000-1-11133−3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000002−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ3622-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−32-222-2-2-1-1110033−3−3000−22-113−3000000-1-11133−3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ3722-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−3-22-2-222-1-1110033−3−30002−21-1−3300000011-1-1−3−333ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ3822-2-22-120021-112-2-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−3-22-2-222-1-1110033−3−3000−221-1−3300000011-1-1−3−333−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000002−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ3922-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−332-222-2-2-1-11100−3−3330002−2-11−33000000-1-111−3−333ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000002−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ4022-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−332-222-2-2-1-11100−3−333000−22-11−33000000-1-111−3−333−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ4122-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−33-22-2-222-1-11100−3−3330002−21-13−300000011-1-133−3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ4222-2-22-120021-112-2-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−33-22-2-222-1-11100−3−333000−221-13−300000011-1-133−3−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000002−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ432-22-22222-2-22-2-2-222-2-222-2-2222-2-2-2-222-2-2222-2222-22-2-2-2-20000002-2-222-22-22-22-200000002-22-2000000000000000000000000002-22-22-20000000000000000
χ442-22-22222-2-22-2-2-222-2-222-2-2222-2-2-2-222-2-2222-2222-22-2-2-2-20000002-2-222-22-22-2-220000000-22-2200000000000000000000000000-22-22-220000000000000000
χ452-22-2222-22-22-2-2-222-2-2-2-222222-2-2-2-222-2-22-2-22-2-2-22-222220000002-2-22-22-22-220000000000000000000000000000000000000000000002i−2i002i−2i2i−2i00000000
χ462-22-2222-22-22-2-2-222-2-2-2-222222-2-2-2-222-2-22-2-22-2-2-22-222220000002-2-22-22-22-22000000000000000000000000000000000000000000000−2i2i00−2i2i−2i2i00000000
χ472-22-222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-12-1122-11-11-2-2-2003−33−3-111-1-11-11-112-20000000-11-113−33−33−33−33−300000000000000002-2-11-1100003−3−3300000000
χ482-22-222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-12-1122-11-11-2-2-2003−33−3-111-1-11-11-11-2200000001-11-13−33−33−33−33−30000000000000000-221-11-10000−333−300000000
χ492-22-222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-12-1122-11-11-2-2-200−33−33-111-1-11-11-112-20000000-11-11−33−33−33−33−3300000000000000002-2-11-110000−333−300000000
χ502-22-222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-12-1122-11-11-2-2-200−33−33-111-1-11-11-11-2200000001-11-1−33−33−33−33−330000000000000000-221-11-100003−3−3300000000
χ512-22-222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-1-21-1-2-21-11-1222003−33−3-111-11-11-11-1000000000−i3i3i3−i3−333−33−3−33−33000000000000000000−i3i3i3−i32i−2i00−ii−ii00000000
χ522-22-222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-1-21-1-2-21-11-1222003−33−3-111-11-11-11-1000000000i3−i3−i3i3−333−33−3−33−33000000000000000000i3−i3−i3i3−2i2i00i−ii−i00000000
χ532-22-222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-1-21-1-2-21-11-122200−33−33-111-11-11-11-1000000000−i3i3i3−i33−3−33−333−33−3000000000000000000−i3i3i3−i3−2i2i00i−ii−i00000000
χ542-22-222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-1-21-1-2-21-11-122200−33−33-111-11-11-11-1000000000i3−i3−i3i33−3−33−333−33−3000000000000000000i3−i3−i3i32i−2i00−ii−ii00000000
χ552-22-2-1222-212-2-2-2-121-222-2-2-1-121111-12-2-2-1-12-2-1-12-22-2111000000-111-1-11-11-112-200000002-22-2000000000000003−33−33−33−33−33−3-11-11-1100000000000003−30
χ562-22-2-1222-212-2-2-2-121-222-2-2-1-121111-12-2-2-1-12-2-1-12-22-2111000000-111-1-11-11-112-200000002-22-200000000000000−33−33−33−33−33−33-11-11-110000000000000−330
χ572-22-2-1222-212-2-2-2-121-222-2-2-1-121111-12-2-2-1-12-2-1-12-22-2111000000-111-1-11-11-11-220000000-22-22000000000000003−33−33−33−33−33−31-11-11-10000000000000−330
χ582-22-2-1222-212-2-2-2-121-222-2-2-1-121111-12-2-2-1-12-2-1-12-22-2111000000-111-1-11-11-11-220000000-22-2200000000000000−33−33−33−33−33−331-11-11-100000000000003−30
χ5944444-2-2444-2-2-2-24-24-2-2-2-2-2-2-21-2-2-2-2-2111-24-2-2-2-211114-2-244-2-2-2-21111-2-2111100400-2-2-2-20000-2-21111111100000000000000000000000000000000000000
χ6044444-2-2444-2-2-2-24-24-2-2-2-2-2-2-21-2-2-2-2-2111-24-2-2-2-211114-2-2-4-422221111-2-2111100-4002222000022-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ6144444-2-2-4-44-2-2-2-24-24-22222-2-21-2-2-2-2-2111-2-42222-1-1-1-1-42244-2-2-2-2111122-1-1-1-100-400-2-2220000221111-1-1-1-100000000000000000000000000000000000000
χ6244444-2-2-4-44-2-2-2-24-24-22222-2-21-2-2-2-2-2111-2-42222-1-1-1-1-422-4-42222111122-1-1-1-10040022-2-20000-2-2-1-1-1-1111100000000000000000000000000000000000000
χ634444-244-4-4-24444-24-24-4-4-4-4-2-24-2-2-2-2-2444-22-4-422-4-4-4-4222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ644444-24-244-2444-2-2-2-2-24444-21-2-2-211-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-20000001111111111440000000-2-2-2-200000000000000000000000000-2-211110000000000000000
χ654444-24-244-2444-2-2-2-2-24444-21-2-2-211-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-20000001111111111-4-4000000022220000000000000000000000000022-1-1-1-10000000000000000
χ664444-24-2-4-4-2444-2-2-2-2-2-4-4-4-4-21-2-2-211-2-2-2-212222222222220000001111-1-1-1-1-1-1000000000−2i3−2i32i32i30000000000000000000000000000i3i3−i3−i30000000000000000
χ674444-24-2-4-4-2444-2-2-2-2-2-4-4-4-4-21-2-2-211-2-2-2-212222222222220000001111-1-1-1-1-1-10000000002i32i3−2i3−2i30000000000000000000000000000−i3−i3i3i30000000000000000
χ684444-2-2444-2-2-2-24-24-24-2-2-2-21-2-211-2-21-2-2-2-2-24411-2-2-2-2-2110000001111-2-2111100044000000000000000000-2-2-2-2-2-2-2-2111111110000000000000000000000
χ694444-2-2444-2-2-2-24-24-24-2-2-2-21-2-211-2-21-2-2-2-2-24411-2-2-2-2-2110000001111-2-21111000-4-400000000000000000022222222-1-1-1-1-1-1-1-10000000000000000000000
χ704444-2-24-4-4-2-2-2-24-24-2422221-2-211-2-21-2-2-2-22-4-4-1-122222-1-1000000111122-1-1-1-1000000000000000000000002323−23−230000−3−3−3−333330000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.