Finite Group Databasebeta

← Group #13156483

Character table — Group #13156483

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order12223334466666666612121212333666666666121212121212121212121212441212121236661212121212122446666666688121212121212121212122424242424242424242424242424242412121212121244881212121224242424412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-200-2-2-2-2-2-2-2-200220000222200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22002222222200-2-20000-2-2-2-200000000000000000000000000000000000000
χ11222222-1222222-12-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-10022-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ12222222-1222222-12-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-222-1-1-1-1-1-100221111-1-1-1-10000000000000000-2-21111-2-200111100000000
χ13222222-1222222-12-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-222-2-211111100-2-2-1-1-1-11111000000000000000022-1-1-1-1-2-200111100000000
χ14222222-1222222-12-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211111100-2-2111111110000000000000000-2-211112200-1-1-1-100000000
χ15222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-200-2-21111110022−i3−i3i3i3-1-1-1-1000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ16222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-200-2-21111110022i3i3−i3−i3-1-1-1-1000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ17222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120022-1-1-1-1-1-100-2-2−i3−i3i3i31111000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ18222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120022-1-1-1-1-1-100-2-2i3i3−i3−i31111000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ1922222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-1-122-1-1-1-122-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ2022222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-1-122-1-1-1-1-2-2-1-10000-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ2122222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-20011-2-21111221100001111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ2222222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-20011-2-21111-2-211000011111111-2-2-2-21111111100000000220000-1-1-1-10000
χ2322222-12-2-2-1-12-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-211222222-1-1-1-1-2-21111-20011-2-2111100-1-10000-1-1-1-133−3−300003333−3−3−3−30000000000000033−3−30000
χ2422222-12-2-2-1-12-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-211222222-1-1-1-1-2-21111-20011-2-2111100-1-10000-1-1-1-1−3−3330000−3−3−3−3333300000000000000−3−3330000
χ2522222-12-2-2-1-12-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-21111200-1-122-1-1-1-100110000111133−3−300003333−3−3−3−300000000000000−3−3330000
χ2622222-12-2-2-1-12-1222221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-21111200-1-122-1-1-1-1001100001111−3−3330000−3−3−3−333330000000000000033−3−30000
χ272222-1222222-122-12-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022000000002200222200002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ282222-1222222-122-12-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-102200000000-2-20022220000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ292222-1222222-122-12-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-2000000002200-2-2-2-200002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ302222-1222222-122-12-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-200000000-2-200-2-2-2-20000-2-2-2-21111111111111111110000000000002-1-10
χ312-22-2222002-2-2-2-2-2-22200002222-222-2-2-2-2-20000000000002i−2i2i2i−2i−2i22-2-200000000000000000−i2i22i−2i00002i2i−2i−2i−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000002−200002−22−20000
χ322-22-2222002-2-2-2-2-2-22200002222-222-2-2-2-2-20000000000002i−2i2i2i−2i−2i22-2-200000000000000000i2−i22i−2i00002i2i−2i−2ii2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000−220000−22−220000
χ332-22-2222002-2-2-2-2-2-22200002222-222-2-2-2-2-2000000000000−2i2i−2i−2i2i2i22-2-200000000000000000−i2i2−2i2i0000−2i−2i2i2i−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000−220000−22−220000
χ342-22-2222002-2-2-2-2-2-22200002222-222-2-2-2-2-2000000000000−2i2i−2i−2i2i2i22-2-200000000000000000i2−i2−2i2i0000−2i−2i2i2ii2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000002−200002−22−20000
χ352-22-22-1200-11-21-2-2-2223−33−3-12-1-112-111-21-20003−333−3−303−32i−2i2i2i−2i−2i-1-1110033−3−3000−i3i300−i3−i3i3i3−i2i2−ii0000−i−iiiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000002−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ362-22-22-1200-11-21-2-2-2223−33−3-12-1-112-111-21-20003−333−3−303−32i−2i2i2i−2i−2i-1-1110033−3−3000−i3i300−i3−i3i3i3i2−i2−ii0000−i−iii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ372-22-22-1200-11-21-2-2-2223−33−3-12-1-112-111-21-20003−333−3−303−3−2i2i−2i−2i2i2i-1-1110033−3−3000i3−i300i3i3−i3−i3−i2i2i−i0000ii−i−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ382-22-22-1200-11-21-2-2-2223−33−3-12-1-112-111-21-20003−333−3−303−3−2i2i−2i−2i2i2i-1-1110033−3−3000i3−i300i3i3−i3−i3i2−i2i−i0000ii−i−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000002−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ392-22-22-1200-11-21-2-2-222−33−33-12-1-112-111-21-2000−33−3−3330−332i−2i2i2i−2i−2i-1-11100−3−333000i3−i300i3i3−i3−i3−i2i2−ii0000−i−iiiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000002−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ402-22-22-1200-11-21-2-2-222−33−33-12-1-112-111-21-2000−33−3−3330−332i−2i2i2i−2i−2i-1-11100−3−333000i3−i300i3i3−i3−i3i2−i2−ii0000−i−iii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ412-22-22-1200-11-21-2-2-222−33−33-12-1-112-111-21-2000−33−3−3330−33−2i2i−2i−2i2i2i-1-11100−3−333000−i3i300−i3−i3i3i3−i2i2i−i0000ii−i−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ422-22-22-1200-11-21-2-2-222−33−33-12-1-112-111-21-2000−33−3−3330−33−2i2i−2i−2i2i2i-1-11100−3−333000−i3i300−i3−i3i3i3i2−i2i−i0000ii−i−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000002−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ432-2-222222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2222-2-22-2-2-22-22-22220000002-2-222-22-22-202i−2i0000000000002i−2i2i−2i000000000000000000002i−2i2i−2i2i−2i0000000000000000
χ442-2-222222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2222-2-22-2-2-22-22-22220000002-2-222-22-22-20−2i2i000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i−2i2i0000000000000000
χ452-2-22222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2222-22-2222-22-22-2-2-20000002-2-22-22-22-220000000000000000000000000000000000000000000002i−2i002i−2i2i−2i00000000
χ462-2-22222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2222-22-2222-22-22-2-2-20000002-2-22-22-22-22000000000000000000000000000000000000000000000−2i2i00−2i2i−2i2i00000000
χ472-2-2222-12-2-2-222-1-21-2122-2-22-1-1-2-21112-1-11-2-11-2-2-11-1122200−i3i3−i3i3-111-1-11-11-1102i−2i00−i3i3−i3i3−i3i30000−ii−ii−i3i3−i3i300000000000000002i−2i−ii−ii00003−3−3300000000
χ482-2-2222-12-2-2-222-1-21-2122-2-22-1-1-2-21112-1-11-2-11-2-2-11-1122200−i3i3−i3i3-111-1-11-11-110−2i2i00−i3i3−i3i3−i3i30000i−ii−i−i3i3−i3i30000000000000000−2i2ii−ii−i0000−333−300000000
χ492-2-2222-12-2-2-222-1-21-2122-2-22-1-1-2-21112-1-11-2-11-2-2-11-1122200i3−i3i3−i3-111-1-11-11-1102i−2i00i3−i3i3−i3i3−i30000−ii−iii3−i3i3−i300000000000000002i−2i−ii−ii0000−333−300000000
χ502-2-2222-12-2-2-222-1-21-2122-2-22-1-1-2-21112-1-11-2-11-2-2-11-1122200i3−i3i3−i3-111-1-11-11-110−2i2i00i3−i3i3−i3i3−i30000i−ii−ii3−i3i3−i30000000000000000−2i2ii−ii−i00003−3−3300000000
χ512-2-2222-1-22-2-222-1-21-21-2-2222-1-1-2-21112-1-1121-1221-11-1-2-2-200−i3i3−i3i3-111-11-11-11-100000i3−i3i3−i3i3−i300003−3−33−i3i3−i3i30000000000000000003−3−332i−2i00−ii−ii00000000
χ522-2-2222-1-22-2-222-1-21-21-2-2222-1-1-2-21112-1-1121-1221-11-1-2-2-200−i3i3−i3i3-111-11-11-11-100000i3−i3i3−i3i3−i30000−333−3−i3i3−i3i3000000000000000000−333−3−2i2i00i−ii−i00000000
χ532-2-2222-1-22-2-222-1-21-21-2-2222-1-1-2-21112-1-1121-1221-11-1-2-2-200i3−i3i3−i3-111-11-11-11-100000−i3i3−i3i3−i3i300003−3−33i3−i3i3−i30000000000000000003−3−33−2i2i00i−ii−i00000000
χ542-2-2222-1-22-2-222-1-21-21-2-2222-1-1-2-21112-1-1121-1221-11-1-2-2-200i3−i3i3−i3-111-11-11-11-100000−i3i3−i3i3−i3i30000−333−3i3−i3i3−i3000000000000000000−333−32i−2i00−ii−ii00000000
χ552-2-22-1222-2-2-2-1221-21-222-2-2-1-12111-2-2-1-12112-2112-22-2-1-1-1000000-111-1-11-11-1102i−2i0000000000002i−2i2i−2i00000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−ii−ii−ii00000000000003−30
χ562-2-22-1222-2-2-2-1221-21-222-2-2-1-12111-2-2-1-12112-2112-22-2-1-1-1000000-111-1-11-11-1102i−2i0000000000002i−2i2i−2i00000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3−ii−ii−ii0000000000000−330
χ572-2-22-1222-2-2-2-1221-21-222-2-2-1-12111-2-2-1-12112-2112-22-2-1-1-1000000-111-1-11-11-110−2i2i000000000000−2i2i−2i2i00000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3i−ii−ii−i0000000000000−330
χ582-2-22-1222-2-2-2-1221-21-222-2-2-1-12111-2-2-1-12112-2112-22-2-1-1-1000000-111-1-11-11-110−2i2i000000000000−2i2i−2i2i00000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i−ii−ii−i00000000000003−30
χ5944444-2-244-2-24-2-24-24-2-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2-211114-2-244-2-2-2-21111-2-21111400-2-2-2-2111100-2-20000111100000000000000000000000000000000000000
χ6044444-2-244-2-24-2-24-24-2-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2-211114-2-2-4-422221111-2-21111-4002222-1-1-1-100220000-1-1-1-100000000000000000000000000000000000000
χ6144444-2-2-4-4-2-24-2-24-24-22222-2-21-2-2-211-2-21-2-42222-1-1-1-1-42244-2-2-2-2111122-1-1-1-1-4002222-1-1-1-100-2-20000111100000000000000000000000000000000000000
χ6244444-2-2-4-4-2-24-2-24-24-22222-2-21-2-2-211-2-21-2-42222-1-1-1-1-422-4-42222111122-1-1-1-1400-2-2-2-2111100220000-1-1-1-100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.