Finite Group Databasebeta

← Group #11921300

Character table — Group #11921300

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444444444444466666688888888888812121212121616161616161616161616161616161624242424242424242424242436364848484872
order122234466622336666666666121244888833666666121212124441212666666666666121212124121212242424242424242488121212124
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−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−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
χ4111111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1−1−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
χ5111111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+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
χ6111111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1−1+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
χ71111111111-1-111-1-1-1-1111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111111111-1-1-1-1-1
χ81111111111-1-111-1-1-1-11111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-111111
χ91111111111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−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−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+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
χ101111111111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1−1−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−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1−1−i32−1−i32−1+i32−1+i321
χ111111111111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+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+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−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
χ121111111111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1−1+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+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1−1+i32−1+i32−1−i32−1−i321
χ1322222-2-222200220000222222-2-222000022222222-2-2-2-2-20022000000000000-2-2-2-20-200000000000000000
χ1422222-2-222200−1−i3−1+i30000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-2220000−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-200220000000000001+i31+i31−i31−i30-200000000000000000
χ1522222-2-222200−1+i3−1−i30000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-2220000−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-200220000000000001−i31−i31+i31+i30-200000000000000000
χ162222-122-1-1-12222-1-1-1-1222222-1-1220000-1-1-1-1-1-1-1-12222200-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1000000000000000
χ172222-122-1-1-122−1−i3−1+i3-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-12200001+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
χ182222-122-1-1-122−1+i3−1−i3-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-12200001−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
χ192222-122-1-1-1-2-2221111222222-1-1220000-1-1-1-1-1-1-1-12222200-1-1-2-2-2-211111111-1-1-1-1-2-111000000000000000
χ202222-122-1-1-1-2-2−1−i3−1+i31111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-12200001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i3200-1-11+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-2-111000000000000000
χ212222-122-1-1-1-2-2−1+i3−1−i31111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-12200001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i3200-1-11−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-2-111000000000000000
χ222222-1-2-2-1-1-10022−i3−i3i3i322222211220000-1-1-1-1-1-1-1-1-2-2-2-2-200-1-10000−i3−i3i3i3−i3−i3i3i3111101−i3i3000000000000000
χ232222-1-2-2-1-1-10022i3i3−i3−i322222211220000-1-1-1-1-1-1-1-1-2-2-2-2-200-1-10000i3i3−i3−i3i3i3−i3−i3111101i3−i3000000000000000
χ242222-1-2-2-1-1-100−1−i3−1+i3−i3−i3i3i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3112200001+i321−i321+i321+i321−i321−i321+i321−i321+i31−i31+i31−i3-200-1-10000−3+i32−3+i323−i323−i323+i323+i32−3−i32−3−i32−1−i32−1−i32−1+i32−1+i3201−i3i3000000000000000
χ252222-1-2-2-1-1-100−1−i3−1+i3i3i3−i3−i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3112200001+i321−i321+i321+i321−i321−i321+i321−i321+i31−i31+i31−i3-200-1-100003−i323−i32−3+i32−3+i32−3−i32−3−i323+i323+i32−1−i32−1−i32−1+i32−1+i3201i3−i3000000000000000
χ262222-1-2-2-1-1-100−1+i3−1−i3−i3−i3i3i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3112200001−i321+i321−i321−i321+i321+i321−i321+i321−i31+i31−i31+i3-200-1-100003+i323+i32−3−i32−3−i32−3+i32−3+i323−i323−i32−1+i32−1+i32−1−i32−1−i3201−i3i3000000000000000
χ272222-1-2-2-1-1-100−1+i3−1−i3i3i3−i3−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3112200001−i321+i321−i321−i321+i321+i321−i321+i321−i31+i31−i31+i3-200-1-10000−3−i32−3−i323+i323+i323−i323−i32−3+i32−3+i32−1+i32−1+i32−1−i32−1−i3201i3−i3000000000000000
χ2822-2-2200-2-220022000022-2-2-2-2002-2−i2−i2i2i2222-22-2-2-200000002-200000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i200000
χ2922-2-2200-2-220022000022-2-2-2-2002-2i2i2−i2−i2222-22-2-2-200000002-200000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i200000
χ3022-2-2200-2-2200−1−i3−1+i30000−1−i3−1+i31+i31−i31+i31−i3002-2−i2−i2i2i2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000002-200000000000000000000ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ5−ζ23−i2i200000
χ3122-2-2200-2-2200−1−i3−1+i30000−1−i3−1+i31+i31−i31+i31−i3002-2i2i2−i2−i2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000002-200000000000000000000−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23i2−i200000
χ3222-2-2200-2-2200−1+i3−1−i30000−1+i3−1−i31−i31+i31−i31+i3002-2−i2−i2i2i2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000002-200000000000000000000ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13−i2i200000
χ3322-2-2200-2-2200−1+i3−1−i30000−1+i3−1−i31−i31+i31−i31+i3002-2i2i2−i2−i2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000002-200000000000000000000−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13i2−i200000
χ342-2-222-222-2-22-2-1-12-22-211-1-1112-2002i−2i2i−2i-1-11111-1-1-1-11102i−2i001-11-11-11-11-11-11-11-10000i−ii−ii−ii−i00i−ii−i0
χ352-2-222-222-2-22-2-1-12-22-211-1-1112-200−2i2i−2i2i-1-11111-1-1-1-1110−2i2i001-11-11-11-11-11-11-11-10000−ii−ii−ii−ii00−ii−ii0
χ362-2-222-222-2-22-21+i321−i322-22-2−1−i32−1+i321+i321−i32−1−i32−1+i322-2002i−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
χ372-2-222-222-2-22-21+i321−i322-22-2−1−i32−1+i321+i321−i32−1−i32−1+i322-200−2i2i−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
χ382-2-222-222-2-22-21−i321+i322-22-2−1+i32−1−i321−i321+i32−1+i32−1−i322-2002i−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
χ392-2-222-222-2-22-21−i321+i322-22-2−1+i32−1−i321−i321+i32−1+i32−1−i322-200−2i2i−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
χ402-2-222-222-2-2-22-1-1-22-2211-1-1112-2002i−2i2i−2i-1-11111-1-1-1-1110−2i2i00-11-11-11-11-11-111-11-10000i−ii−ii−ii−i00−ii−ii0
χ412-2-222-222-2-2-22-1-1-22-2211-1-1112-200−2i2i−2i2i-1-11111-1-1-1-11102i−2i00-11-11-11-11-11-111-11-10000−ii−ii−ii−ii00i−ii−i0
χ422-2-222-222-2-2-221+i321−i32-22-22−1−i32−1+i321+i321−i32−1−i32−1+i322-2002i−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+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i320000ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ1400−ζ22ζ22−ζ14ζ140
χ432-2-222-222-2-2-221+i321−i32-22-22−1−i32−1+i321+i321−i32−1−i32−1+i322-200−2i2i−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+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i320000−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ1400ζ22−ζ22ζ14−ζ140
χ442-2-222-222-2-2-221−i321+i32-22-22−1+i32−1−i321−i321+i32−1+i32−1−i322-2002i−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−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i320000ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ2200−ζ14ζ14−ζ22ζ220
χ452-2-222-222-2-2-221−i321+i32-22-22−1+i32−1−i321−i321+i32−1+i32−1−i322-200−2i2i−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−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i320000−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ2200ζ14−ζ14ζ22−ζ220
χ4633333333333300333300000033-1-13333000000000000-133-1-10000000000000000-1-1-1-100000000-1-10000-1
χ4733333333333300333300000033-1-1-3-3-3-3000000000000-1-3-3-1-10000000000000000-1-1-1-1000000001100001
χ483333333333-3-300-3-3-3-300000033-1-13333000000000000-1-3-3-1-100000000000000001-11100000000-1-100001
χ493333333333-3-300-3-3-3-300000033-1-1-3-3-3-3000000000000-133-1-100000000000000001-11100000000110000-1
χ5044-4-4-20022-20044000044-4-4-4-4004-40000-2-2-22-22220000000-2200000000000000000000000000000000000
χ5144-4-4-20022-200−2−2i3−2+2i30000−2−2i3−2+2i32+2i32−2i32+2i32−2i3004-400001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i30000000-2200000000000000000000000000000000000
χ5244-4-4-20022-200−2+2i3−2−2i30000−2+2i3−2−2i32−2i32+2i32−2i32+2i3004-400001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i30000000-2200000000000000000000000000000000000
χ534-44-4400-44-400-2-200002222-2-2000022−22−2222-2-22-22-222000000000000000000000000000002−2−222−2−220000000
χ544-44-4400-44-400-2-200002222-2-20000−222222−22-2-22-22-22200000000000000000000000000000−222−2−222−20000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.