Finite Group Databasebeta

← Group #13155884

Character table — Group #13155884

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order1222333446666666661212121233366666666612121212121212121212121244121212123666121212121212222666666666666881212121212122424242424242424242424242424242466666644881212121224242424412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-200-2-2-2-20000-2-2-2-20022222200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-220022220000222200-2-2-2-2-2-200000000000000000000000000000000000000
χ11222222-122222-1-1222-122222-1-122-1-1-1-12-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-10022-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ12222222-122222-1-1222-122222-1-122-1-1-1-12-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-222-1-11111-1-1-1-10022-1-1-1-10000000000000000-2-21111-2-200111100000000
χ13222222-122222-1-1222-122222-1-122-1-1-1-12-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-222-2-211-1-1-1-1111100-2-21111000000000000000022-1-1-1-1-2-200111100000000
χ14222222-122222-1-1222-122222-1-122-1-1-1-12-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2111111111100-2-211110000000000000000-2-211112200-1-1-1-100000000
χ15222222-1-2-2222-1-1222-1-2-2-2-22-1-122-1-1-1-12-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-200-2-211−i3−i3i3i311110022-1-1-1-1000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ16222222-1-2-2222-1-1222-1-2-2-2-22-1-122-1-1-1-12-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-200-2-211i3i3−i3−i311110022-1-1-1-1000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ17222222-1-2-2222-1-1222-1-2-2-2-22-1-122-1-1-1-12-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120022-1-1−i3−i3i3i3-1-1-1-100-2-21111000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ18222222-1-2-2222-1-1222-1-2-2-2-22-1-122-1-1-1-12-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120022-1-1i3i3−i3−i3-1-1-1-100-2-21111000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ1922222-122222-122-12-122222-12-1-1-122-1-1-1-12-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022000022220000220000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ2022222-122222-122-12-122222-12-1-1-122-1-1-1-12-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022000022220000-2-2000000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ2122222-122222-122-12-122222-12-1-1-122-1-1-1-12-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-20000-2-2-2-20000220000002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ2222222-122222-122-12-122222-12-1-1-122-1-1-1-12-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-20000-2-2-2-20000-2-2000000-2-2-2-21111111111111111110000000000002-1-10
χ232222-12222-1-12222-122-1-1-1-1-1-12-1-1-1-122-12-1222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-1-1220000-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ242222-12222-1-12222-122-1-1-1-1-1-12-1-1-1-122-12-1222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-1-1220000-1-1-1-1-2-2-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ252222-12222-1-12222-122-1-1-1-1-1-12-1-1-1-122-12-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-20011-2-20000111122111111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ262222-12222-1-12222-122-1-1-1-1-1-12-1-1-1-122-12-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-20011-2-200001111-2-21111111111-2-2-2-21111111100000000220000-1-1-1-10000
χ272222-122-2-2-1-12222-1221111-1-12-1-1-1-122-12-1-2-2-2111111-211222222-1-1-1-1-2-21111-20011-2-20000111100-1-1-1-1-1-133−3−300003333−3−3−3−30000000000000033−3−30000
χ282222-122-2-2-1-12222-1221111-1-12-1-1-1-122-12-1-2-2-2111111-211222222-1-1-1-1-2-21111-20011-2-20000111100-1-1-1-1-1-1−3−3330000−3−3−3−3333300000000000000−3−3330000
χ292222-122-2-2-1-12222-1221111-1-12-1-1-1-122-12-1-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-21111200-1-1220000-1-1-1-10011111133−3−300003333−3−3−3−300000000000000−3−3330000
χ302222-122-2-2-1-12222-1221111-1-12-1-1-1-122-12-1-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-21111200-1-1220000-1-1-1-100111111−3−3330000−3−3−3−333330000000000000033−3−30000
χ312-22-2222002-2-22-2-2-22-200002222-22-22-2-2-2-20000000000002i−2i2i2i−2i−2i22-2-20000000000000000000002−22i−2i2i2i−2i−2i2−22−222−2−222−2−222−2−200000000−i2i20000−i2i2−i2i20000
χ322-22-2222002-2-22-2-2-22-200002222-22-22-2-2-2-20000000000002i−2i2i2i−2i−2i22-2-2000000000000000000000−222i−2i2i2i−2i−2i−22−22−2−222−2−222−2−22200000000i2−i20000i2−i2i2−i20000
χ332-22-2222002-2-22-2-2-22-200002222-22-22-2-2-2-2000000000000−2i2i−2i−2i2i2i22-2-20000000000000000000002−2−2i2i−2i−2i2i2i2−22−222−2−222−2−222−2−200000000i2−i20000i2−i2i2−i20000
χ342-22-2222002-2-22-2-2-22-200002222-22-22-2-2-2-2000000000000−2i2i−2i−2i2i2i22-2-2000000000000000000000−22−2i2i−2i−2i2i2i−22−22−2−222−2−222−2−22200000000−i2i20000−i2i2−i2i20000
χ352-22-2-12200-11-22-2-212-23−33−3-1-12-11-112-21-210003−333−3−303−32i−2i2i2i−2i−2i-1-1110033−3−3000−i3i3000000−i3−i3i3i32−2−ii−i−iiiζ5−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
χ362-22-2-12200-11-22-2-212-23−33−3-1-12-11-112-21-210003−333−3−303−32i−2i2i2i−2i−2i-1-1110033−3−3000−i3i3000000−i3−i3i3i3−22−ii−i−iii−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
χ372-22-2-12200-11-22-2-212-23−33−3-1-12-11-112-21-210003−333−3−303−3−2i2i−2i−2i2i2i-1-1110033−3−3000i3−i3000000i3i3−i3−i32−2i−iii−i−iζ5−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
χ382-22-2-12200-11-22-2-212-23−33−3-1-12-11-112-21-210003−333−3−303−3−2i2i−2i−2i2i2i-1-1110033−3−3000i3−i3000000i3i3−i3−i3−22i−iii−i−i−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
χ392-22-2-12200-11-22-2-212-2−33−33-1-12-11-112-21-21000−33−3−3330−332i−2i2i2i−2i−2i-1-11100−3−333000i3−i3000000i3i3−i3−i32−2−ii−i−iiiζ13−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
χ402-22-2-12200-11-22-2-212-2−33−33-1-12-11-112-21-21000−33−3−3330−332i−2i2i2i−2i−2i-1-11100−3−333000i3−i3000000i3i3−i3−i3−22−ii−i−iii−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
χ412-22-2-12200-11-22-2-212-2−33−33-1-12-11-112-21-21000−33−3−3330−33−2i2i−2i−2i2i2i-1-11100−3−333000−i3i3000000−i3−i3i3i32−2i−iii−i−iζ13−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
χ422-22-2-12200-11-22-2-212-2−33−33-1-12-11-112-21-21000−33−3−3330−33−2i2i−2i−2i2i2i-1-11100−3−333000−i3i3000000−i3−i3i3i3−22i−iii−i−i−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
χ432-2-222222-2-2-2-2-2-222-2222-2-2222-2-2-2-2-2-2222-22-2-2-22-22-22220000002-2-222-22-22-20000000000000000000000000000000000000000000002-2002-22-200000000
χ442-2-222222-2-2-2-2-2-222-2222-2-2222-2-2-2-2-2-2222-22-2-2-22-22-22220000002-2-222-22-22-2000000000000000000000000000000000000000000000-2200-22-2200000000
χ452-2-22222-22-2-2-2-2-222-22-2-222222-2-2-2-2-2-22222-2222-22-22-2-2-20000002-2-22-22-22-2202-200002-22-200000000000000000000000000002-22-22-20000000000000000
χ462-2-22222-22-2-2-2-2-222-22-2-222222-2-2-2-2-2-22222-2222-22-22-2-2-20000002-2-22-22-22-220-220000-22-220000000000000000000000000000-22-22-220000000000000000
χ472-2-2222-12-2-2-2-21122-2-122-2-22-1-1-2-211112-1-1-2-11-2-2-11-1122200−i3i3−i3i3-111-1-11-11-1100000−i3i3−i3i3i3−i3−i3i3−i3i30000−i3i3−i3i3000000000000000000−i3i3i3−i32-200-11-1100000000
χ482-2-2222-12-2-2-2-21122-2-122-2-22-1-1-2-211112-1-1-2-11-2-2-11-1122200−i3i3−i3i3-111-1-11-11-1100000−i3i3i3−i3−i3i3−i3i3−i3i30000−i3i3−i3i3000000000000000000i3−i3−i3i3-22001-11-100000000
χ492-2-2222-12-2-2-2-21122-2-122-2-22-1-1-2-211112-1-1-2-11-2-2-11-1122200i3−i3i3−i3-111-1-11-11-1100000i3−i3−i3i3i3−i3i3−i3i3−i30000i3−i3i3−i3000000000000000000−i3i3i3−i3-22001-11-100000000
χ502-2-2222-12-2-2-2-21122-2-122-2-22-1-1-2-211112-1-1-2-11-2-2-11-1122200i3−i3i3−i3-111-1-11-11-1100000i3−i3i3−i3−i3i3i3−i3i3−i30000i3−i3i3−i3000000000000000000i3−i3−i3i32-200-11-1100000000
χ512-2-2222-1-22-2-2-21122-2-1-2-2222-1-1-2-211112-1-121-1221-11-1-2-2-200−i3i3−i3i3-111-11-11-11-102-200i3−i3-11-11i3−i3i3−i30000−i3i3−i3i300000000000000002-2-11-110000−i3i3i3−i300000000
χ522-2-2222-1-22-2-2-21122-2-1-2-2222-1-1-2-211112-1-121-1221-11-1-2-2-200−i3i3−i3i3-111-11-11-11-10-2200i3−i31-11-1i3−i3i3−i30000−i3i3−i3i30000000000000000-221-11-10000i3−i3−i3i300000000
χ532-2-2222-1-22-2-2-21122-2-1-2-2222-1-1-2-211112-1-121-1221-11-1-2-2-200i3−i3i3−i3-111-11-11-11-102-200−i3i3-11-11−i3i3−i3i30000i3−i3i3−i300000000000000002-2-11-110000i3−i3−i3i300000000
χ542-2-2222-1-22-2-2-21122-2-1-2-2222-1-1-2-211112-1-121-1221-11-1-2-2-200i3−i3i3−i3-111-11-11-11-10-2200−i3i31-11-1−i3i3−i3i30000i3−i3i3−i30000000000000000-221-11-10000−i3i3i3−i300000000
χ552-2-222-12-22-2-21-2-2-1212-2-222-12-111-2-211-1-12-1-22-1-1-22-22111000000-111-11-11-11-102-200002-22-200000000000000003−33−33−33−33−33−3-11-11-1100000000000003−30
χ562-2-222-12-22-2-21-2-2-1212-2-222-12-111-2-211-1-12-1-22-1-1-22-22111000000-111-11-11-11-102-200002-22-20000000000000000−33−33−33−33−33−33-11-11-110000000000000−330
χ572-2-222-12-22-2-21-2-2-1212-2-222-12-111-2-211-1-12-1-22-1-1-22-22111000000-111-11-11-11-10-220000-22-2200000000000000003−33−33−33−33−33−31-11-11-10000000000000−330
χ582-2-222-12-22-2-21-2-2-1212-2-222-12-111-2-211-1-12-1-22-1-1-22-22111000000-111-11-11-11-10-220000-22-220000000000000000−33−33−33−33−33−331-11-11-100000000000003−30
χ5944444-24-4-444-244-24-24-4-4-4-4-24-2-2-244-2-2-2-242-4-422-4-4-4-4222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ6044444-2-24444-2-2-2-24-2-24444-2-21-2-2-2-211-21-2-2-2-2-2-2-2-2-2-2-2-2-200000011111111110440000-2-2-2-20000000000000000000000000000-2-211110000000000000000
χ6144444-2-24444-2-2-2-24-2-24444-2-21-2-2-2-211-21-2-2-2-2-2-2-2-2-2-2-2-2-200000011111111110-4-400002222000000000000000000000000000022-1-1-1-10000000000000000
χ6244444-2-2-4-444-2-2-2-24-2-2-4-4-4-4-2-21-2-2-2-211-21-22222222222220000001111-1-1-1-1-1-10000000−2i3−2i32i32i3000000000000000000000000000000i3i3−i3−i30000000000000000
χ6344444-2-2-4-444-2-2-2-24-2-2-4-4-4-4-2-21-2-2-2-211-21-22222222222220000001111-1-1-1-1-1-100000002i32i3−2i3−2i3000000000000000000000000000000−i3−i3i3i30000000000000000
χ644444-24-244-2-24-2-24-24-2-2-2-2-2-21-2-2-211-2-2-2-214-2-2-2-211114-2-244-2-2-2-21111-2-21111400-2-2-2-20000111100-2-2111100000000000000000000000000000000000000
χ654444-24-244-2-24-2-24-24-2-2-2-2-2-21-2-2-211-2-2-2-214-2-2-2-211114-2-2-4-422221111-2-21111-40022220000-1-1-1-10022-1-1-1-100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.