Finite Group Databasebeta

← Group #11921312

Character table — Group #11921312

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444444444444466666688888888888812121212121616161616161616161616161616161624242424242424242424242436364848484872
order1222344666334466666612121212121244888833666666121212124441212121212121212121212121212121212124121212242424242424242488121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-111111111-1-1-1-11111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1
χ4111111111111-1-111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321
χ61111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i32-1
χ71111111111−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111+i321+i321−i321−i32-1
χ81111111111−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1−1−i32−1−i32−1+i32−1+i321
χ91111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321
χ101111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i32-1
χ111111111111−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−i321−i321+i321+i32-1
χ121111111111−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1−1+i32−1+i32−1−i32−1−i321
χ1322222-2-22222200222222-2-2000022000022222222-2-2-2-2-200220000-2-2-2-2000000000-200000000000000000
χ1422222-2-2222−1−i3−1+i300−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-20000220000−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-2002200001+i31+i31−i31−i3000000000-200000000000000000
χ1522222-2-2222−1+i3−1−i300−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-20000220000−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-2002200001−i31−i31+i31+i3000000000-200000000000000000
χ162222-122-1-1-12222222222-1-1-1-1-1-1220000-1-1-1-1-1-1-1-12222200-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1000000000000000
χ172222-122-1-1-122-2-2222222-1-11111220000-1-1-1-1-1-1-1-12222200-1-1-2-2-2-2-1-1-1-111111111-2-111000000000000000
χ182222-122-1-1-1−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-1-1-12200001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i3200-1-1−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i322-1-1-1000000000000000
χ192222-122-1-1-1−1−i3−1+i3-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-111112200001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i3200-1-11+i31+i31−i31−i31+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-2-111000000000000000
χ202222-122-1-1-1−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-1-1-12200001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i3200-1-1−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i322-1-1-1000000000000000
χ212222-122-1-1-1−1+i3−1−i3-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-111112200001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i3200-1-11−i31−i31+i31+i31−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-2-111000000000000000
χ222222-1-2-2-1-1-1220022222211−i3−i3i3i3220000-1-1-1-1-1-1-1-1-2-2-2-2-200-1-100001111−i3−i3i3i3−i3−i3i3i301−i3i3000000000000000
χ232222-1-2-2-1-1-1220022222211i3i3−i3−i3220000-1-1-1-1-1-1-1-1-2-2-2-2-200-1-100001111i3i3−i3−i3i3i3−i3−i301i3−i3000000000000000
χ242222-1-2-2-1-1-1−1−i3−1+i300−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311−i3−i3i3i32200001+i321−i321+i321+i321−i321−i321+i321−i321+i31−i31+i31−i3-200-1-10000−1−i32−1−i32−1+i32−1+i32−3+i32−3+i323−i323−i323+i323+i32−3−i32−3−i3201−i3i3000000000000000
χ252222-1-2-2-1-1-1−1−i3−1+i300−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311i3i3−i3−i32200001+i321−i321+i321+i321−i321−i321+i321−i321+i31−i31+i31−i3-200-1-10000−1−i32−1−i32−1+i32−1+i323−i323−i32−3+i32−3+i32−3−i32−3−i323+i323+i3201i3−i3000000000000000
χ262222-1-2-2-1-1-1−1+i3−1−i300−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311−i3−i3i3i32200001−i321+i321−i321−i321+i321+i321−i321+i321−i31+i31−i31+i3-200-1-10000−1+i32−1+i32−1−i32−1−i323+i323+i32−3−i32−3−i32−3+i32−3+i323−i323−i3201−i3i3000000000000000
χ272222-1-2-2-1-1-1−1+i3−1−i300−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311i3i3−i3−i32200001−i321+i321−i321−i321+i321+i321−i321+i321−i31+i31−i31+i3-200-1-10000−1+i32−1+i32−1−i32−1−i32−3−i32−3−i323+i323+i323−i323−i32−3+i32−3+i3201i3−i3000000000000000
χ2822-2-22002-2-2220022-2-2-2-20000002-222−2−2222-22-2-2-200000002-20000000000000000000022−2−222−2−22−200000
χ2922-2-22002-2-2220022-2-2-2-20000002-2−2−222222-22-2-2-200000002-200000000000000000000−2−222−2−222−2200000
χ3022-2-22002-2-2−1−i3−1+i300−1−i3−1+i31+i31−i31+i31−i30000002-222−2−2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000002-200000000000000000000−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ232−200000
χ3122-2-22002-2-2−1−i3−1+i300−1−i3−1+i31+i31−i31+i31−i30000002-2−2−222−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000002-200000000000000000000ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23−2200000
χ3222-2-22002-2-2−1+i3−1−i300−1+i3−1−i31−i31+i31−i31+i30000002-222−2−2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000002-200000000000000000000ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ132−200000
χ3322-2-22002-2-2−1+i3−1−i300−1+i3−1−i31−i31+i31−i31+i30000002-2−2−222−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000002-200000000000000000000−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−2200000
χ342-2-222-22-22-2-1-12-211-1-1112-22-22-2002i−2i2i−2i-1-11111-1-1-1-11102i−2i001-11-11-11-11-11-11-11-10000i−ii−ii−ii−i00i−ii−i0
χ352-2-222-22-22-2-1-12-211-1-1112-22-22-200−2i2i−2i2i-1-11111-1-1-1-1110−2i2i001-11-11-11-11-11-11-11-10000−ii−ii−ii−ii00−ii−ii0
χ362-2-222-22-22-2-1-1-2211-1-1112-2-22-22002i−2i2i−2i-1-11111-1-1-1-1110−2i2i00-11-111-11-1-11-11-11-110000i−ii−ii−ii−i00−ii−ii0
χ372-2-222-22-22-2-1-1-2211-1-1112-2-22-2200−2i2i−2i2i-1-11111-1-1-1-11102i−2i00-11-111-11-1-11-11-11-110000−ii−ii−ii−ii00i−ii−i0
χ382-2-222-22-22-21+i321−i322-2−1−i32−1+i321+i321−i32−1−i32−1+i322-22-22-2002i−2i2i−2i1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1+i3202i−2i00−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i320000ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ1400ζ22−ζ22ζ14−ζ140
χ392-2-222-22-22-21+i321−i322-2−1−i32−1+i321+i321−i32−1−i32−1+i322-22-22-200−2i2i−2i2i1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1+i320−2i2i00−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i320000−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ1400−ζ22ζ22−ζ14ζ140
χ402-2-222-22-22-21+i321−i32-22−1−i32−1+i321+i321−i32−1−i32−1+i322-2-22-22002i−2i2i−2i1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1+i320−2i2i001+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i320000ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ1400−ζ22ζ22−ζ14ζ140
χ412-2-222-22-22-21+i321−i32-22−1−i32−1+i321+i321−i32−1−i32−1+i322-2-22-2200−2i2i−2i2i1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1+i3202i−2i001+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i320000−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ1400ζ22−ζ22ζ14−ζ140
χ422-2-222-22-22-21−i321+i322-2−1+i32−1−i321−i321+i32−1+i32−1−i322-22-22-2002i−2i2i−2i1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1−i3202i−2i00−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i320000ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ2200ζ14−ζ14ζ22−ζ220
χ432-2-222-22-22-21−i321+i322-2−1+i32−1−i321−i321+i32−1+i32−1−i322-22-22-200−2i2i−2i2i1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1−i320−2i2i00−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i320000−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ2200−ζ14ζ14−ζ22ζ220
χ442-2-222-22-22-21−i321+i32-22−1+i32−1−i321−i321+i32−1+i32−1−i322-2-22-22002i−2i2i−2i1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1−i320−2i2i001−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i320000ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ2200−ζ14ζ14−ζ22ζ220
χ452-2-222-22-22-21−i321+i32-22−1+i32−1−i321−i321+i32−1+i32−1−i322-2-22-2200−2i2i−2i2i1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1−i3202i−2i001−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i320000−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ2200ζ14−ζ14ζ22−ζ220
χ4633333333330033000000333333-1-13333000000000000-133-1-10000000000000000-1-1-1-100000000-1-10000-1
χ4733333333330033000000333333-1-1-3-3-3-3000000000000-1-3-3-1-10000000000000000-1-1-1-1000000001100001
χ48333333333300-3-300000033-3-3-3-3-1-13333000000000000-1-3-3-1-100000000000000001-11100000000-1-100001
χ49333333333300-3-300000033-3-3-3-3-1-1-3-3-3-3000000000000-133-1-100000000000000001-11100000000110000-1
χ5044-4-4-200-222440044-4-4-4-40000004-40000-2-2-22-22220000000-2200000000000000000000000000000000000
χ5144-4-4-200-222−2−2i3−2+2i300−2−2i3−2+2i32+2i32−2i32+2i32−2i30000004-400001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i30000000-2200000000000000000000000000000000000
χ5244-4-4-200-222−2+2i3−2−2i300−2+2i3−2−2i32−2i32+2i32−2i32+2i30000004-400001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i30000000-2200000000000000000000000000000000000
χ534-44-4400-4-44-2-2002222-2-200000000−2i22i22i2−2i2-2-22-22-22200000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000000
χ544-44-4400-4-44-2-2002222-2-2000000002i2−2i2−2i22i2-2-22-22-22200000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.