Finite Group Databasebeta

← Group #11921308

Character table — Group #11921308

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444444444444466666688888888888812121212121616161616161616161616161616161624242424242424242424242436364848484872
order1222344666334466666612121212121244888833666666121212124441212121212121212121212121212121212124121212242424242424242488121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1111111-1-1-1-1111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1
χ4111111111111-1-1111111-1-1-1-11111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111
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+i32-1-1-1-111111111−1−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+i32-1-1-1-11111-1-1-1-1−1−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−i32-1-1-1-111111111−1+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−i32-1-1-1-11111-1-1-1-1−1+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
χ1322222-2-222222002222220000-2-222000022222222-2-2-2-2-200220000-2-2-2-2000000000-200000000000000000
χ1422222-2-2222−1−i3−1+i300−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000-2-2220000−1−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−i30000-2-2220000−1+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
χ172222-122-1-1-122-2-22222221111-1-1220000-1-1-1-1-1-1-1-12222200-1-1-2-2-2-2-1-1-1-111111111-2-111000000000000000
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+i31111-1-12200001+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−i31111-1-12200001−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
χ222222-1-2-2-1-1-12200222222−i3−i3i3i311220000-1-1-1-1-1-1-1-1-2-2-2-2-200-1-100001111−i3−i3i3i3−i3−i3i3i301−i3i3000000000000000
χ232222-1-2-2-1-1-12200222222i3i3−i3−i311220000-1-1-1-1-1-1-1-1-2-2-2-2-200-1-100001111i3i3−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+i3−i3−i3i3i3112200001+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+i3i3i3−i3−i3112200001+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−i3−i3−i3i3i3112200001−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−i3i3i3−i3−i3112200001−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
χ282-22-222-2-2-22-1-12i−2i-1-111112i−2i2i−2i2-20022-2-2-1-111-1-11111-1-102i−2i00i−ii−i1-11-1i−ii−ii−ii−i000011-1-111-1-100i−ii−i0
χ292-22-222-2-2-22-1-12i−2i-1-111112i−2i2i−2i2-200-2-222-1-111-1-11111-1-10−2i2i00i−ii−i1-11-1i−ii−ii−ii−i0000-1-111-1-11100−ii−ii0
χ302-22-222-2-2-22-1-1−2i2i-1-11111−2i2i−2i2i2-20022-2-2-1-111-1-11111-1-10−2i2i00−ii−ii1-11-1−ii−ii−ii−ii000011-1-111-1-100−ii−ii0
χ312-22-222-2-2-22-1-1−2i2i-1-11111−2i2i−2i2i2-200-2-222-1-111-1-11111-1-102i−2i00−ii−ii1-11-1−ii−ii−ii−ii0000-1-111-1-11100i−ii−i0
χ322-22-222-2-2-221+i321−i322i−2i1+i321−i32−1−i32−1+i32−1−i32−1+i322i−2i2i−2i2-20022-2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i3202i−2i00ζ22−ζ22ζ14−ζ14−1−i321+i32−1+i321−i32ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ140000−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200ζ22−ζ22ζ14−ζ140
χ332-22-222-2-2-221+i321−i322i−2i1+i321−i32−1−i32−1+i32−1−i32−1+i322i−2i2i−2i2-200-2-2221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i320−2i2i00ζ22−ζ22ζ14−ζ14−1−i321+i32−1+i321−i32ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ1400001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200−ζ22ζ22−ζ14ζ140
χ342-22-222-2-2-221+i321−i32−2i2i1+i321−i32−1−i32−1+i32−1−i32−1+i32−2i2i−2i2i2-20022-2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i320−2i2i00−ζ22ζ22−ζ14ζ14−1−i321+i32−1+i321−i32−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ140000−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200−ζ22ζ22−ζ14ζ140
χ352-22-222-2-2-221+i321−i32−2i2i1+i321−i32−1−i32−1+i32−1−i32−1+i32−2i2i−2i2i2-200-2-2221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i3202i−2i00−ζ22ζ22−ζ14ζ14−1−i321+i32−1+i321−i32−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ1400001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200ζ22−ζ22ζ14−ζ140
χ362-22-222-2-2-221−i321+i322i−2i1−i321+i32−1+i32−1−i32−1+i32−1−i322i−2i2i−2i2-20022-2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i3202i−2i00ζ14−ζ14ζ22−ζ22−1+i321−i32−1−i321+i32ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ220000−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200ζ14−ζ14ζ22−ζ220
χ372-22-222-2-2-221−i321+i322i−2i1−i321+i32−1+i32−1−i32−1+i32−1−i322i−2i2i−2i2-200-2-2221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i320−2i2i00ζ14−ζ14ζ22−ζ22−1+i321−i32−1−i321+i32ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ2200001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200−ζ14ζ14−ζ22ζ220
χ382-22-222-2-2-221−i321+i32−2i2i1−i321+i32−1+i32−1−i32−1+i32−1−i32−2i2i−2i2i2-20022-2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i320−2i2i00−ζ14ζ14−ζ22ζ22−1+i321−i32−1−i321+i32−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ220000−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200−ζ14ζ14−ζ22ζ220
χ392-22-222-2-2-221−i321+i32−2i2i1−i321+i32−1+i32−1−i32−1+i32−1−i32−2i2i−2i2i2-200-2-2221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i3202i−2i00−ζ14ζ14−ζ22ζ22−1+i321−i32−1−i321+i32−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ2200001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200ζ14−ζ14ζ22−ζ220
χ402-2-222002-2-22200-2-2-2-2220000002-2−i2i2−i2i22222-2-2-2-200000002-200000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i200000
χ412-2-222002-2-22200-2-2-2-2220000002-2i2−i2i2−i22222-2-2-2-200000002-200000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i200000
χ422-2-222002-2-2−1−i3−1+i3001+i31−i31+i31−i3−1−i3−1+i30000002-2−i2i2−i2i2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300000002-200000000000000000000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23−i2i200000
χ432-2-222002-2-2−1−i3−1+i3001+i31−i31+i31−i3−1−i3−1+i30000002-2i2−i2i2−i2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300000002-200000000000000000000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23i2−i200000
χ442-2-222002-2-2−1+i3−1−i3001−i31+i31−i31+i3−1+i3−1−i30000002-2−i2i2−i2i2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300000002-200000000000000000000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13−i2i200000
χ452-2-222002-2-2−1+i3−1−i3001−i31+i31−i31+i3−1+i3−1−i30000002-2i2−i2i2−i2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300000002-200000000000000000000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13i2−i200000
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
χ48333333333300-3-3000000-3-3-3-333-1-13333000000000000-1-3-3-1-100000000000000001-11100000000-1-100001
χ49333333333300-3-3000000-3-3-3-333-1-1-3-3-3-3000000000000-133-1-100000000000000001-11100000000110000-1
χ5044-4-4400-44-4-2-20022-2-22200000000−2i22i22i2−2i2-2-22222-2-200000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000000
χ5144-4-4400-44-4-2-20022-2-222000000002i2−2i2−2i22i2-2-22222-2-200000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000000
χ5244-4-4400-44-41+i31−i300−1−i3−1+i31+i31−i3−1−i3−1+i300000000−2i22i22i2−2i21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000000000000000000000000000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ230000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.