Finite Group Databasebeta

← Group #11921381

Character table — Group #11921381

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444444666666668888888888881212121212121212121212121616161616161616161616161616161624242424242424243636363648484848
order124423461212233466666121212121212122244444433666612121212121224666688121212126666666612121212121212121212121212121212448824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1−i32−1+i321111−1−i32−1+i32111−1−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+i32111111111111−1−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+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
χ411111111111−1−i32−1+i321111−1−i32−1+i32111−1−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+i32111111-1-11111−1−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+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321−i321−i32
χ511111111111−1+i32−1−i321111−1+i32−1−i32111−1+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−i32111111111111−1+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−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
χ611111111111−1+i32−1−i321111−1+i32−1−i32111−1+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−i32111111-1-11111−1+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−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321+i321+i32
χ71111111111-111-11-1-1111-1-1111111111111111111111111-1-111-1-1-1-111-1-1-1-11-1-11-1-1-1-11-1-11-1-11111111111-1-1-1-1-1-1
χ81111111111-111-11-1-1111-1-111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-11-1-11-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111
χ91111111111-1−1−i32−1+i32-11-1-1−1−i32−1+i321-1-1−1−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+i32-1-111-1-1-1-111-1-11+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1-11+i321+i321−i321−i32
χ101111111111-1−1−i32−1+i32-11-1-1−1−i32−1+i321-1-1−1−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+i32-1-111-1-11111-1-11+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i32
χ111111111111-1−1+i32−1−i32-11-1-1−1+i32−1−i321-1-1−1+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−i32-1-111-1-1-1-111-1-11−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211-1-11−i321−i321+i321+i32
χ121111111111-1−1+i32−1−i32-11-1-1−1+i32−1−i321-1-1−1+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−i32-1-111-1-11111-1-11−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i32
χ1311-1-1-1111-1-1111-1-111111-1-1-1-1-1-11-11-1ii−i−i1111-1-111-1-1-1-1-111-1-1-1i−i1-11111-111-111-1-11-1-11-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ1411-1-1-1111-1-1111-1-111111-1-1-1-1-1-11-11-1−i−iii1111-1-111-1-1-1-1-111-1-1-1−ii1-11111-111-111-1-11-1-11-1-1−i−iii−i−iii−ii−ii−ii−ii
χ1511-1-1-1111-1-11−1−i32−1+i32-1-111−1−i32−1+i321-1-11+i321+i321−i321−i321-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32-111-1-1-1i−i1-111−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7i−ii−iζ11−ζ11ζ7−ζ7
χ1611-1-1-1111-1-11−1−i32−1+i32-1-111−1−i32−1+i321-1-11+i321+i321−i321−i321-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32-111-1-1-1−ii1-111−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ii−ii−ζ11ζ11−ζ7ζ7
χ1711-1-1-1111-1-11−1+i32−1−i32-1-111−1+i32−1−i321-1-11−i321−i321+i321+i321-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32-111-1-1-1i−i1-111−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11i−ii−iζ7−ζ7ζ11−ζ11
χ1811-1-1-1111-1-11−1+i32−1−i32-1-111−1+i32−1−i321-1-11−i321−i321+i321+i321-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32-111-1-1-1−ii1-111−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ii−ii−ζ7ζ7−ζ11ζ11
χ1911-1-1-1111-1-1-1111-1-1-111111-1-1-1-11-11-1ii−i−i1111-1-111-1-1-1-11-11-111−ii1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−ii−i−ii−ii−ii
χ2011-1-1-1111-1-1-1111-1-1-111111-1-1-1-11-11-1−i−iii1111-1-111-1-1-1-11-11-111i−i1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii−iii−ii−ii−i
χ2111-1-1-1111-1-1-1−1−i32−1+i321-1-1-1−1−i32−1+i321111+i321+i321−i321−i321-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321-11-111−ii1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7i−i−ii−ζ11ζ11−ζ7ζ7
χ2211-1-1-1111-1-1-1−1−i32−1+i321-1-1-1−1−i32−1+i321111+i321+i321−i321−i321-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321-11-111i−i1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−iii−iζ11−ζ11ζ7−ζ7
χ2311-1-1-1111-1-1-1−1+i32−1−i321-1-1-1−1+i32−1−i321111−i321−i321+i321+i321-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321-11-111−ii1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11i−i−ii−ζ7ζ7−ζ11ζ11
χ2411-1-1-1111-1-1-1−1+i32−1−i321-1-1-1−1+i32−1−i321111−i321−i321+i321+i321-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321-11-111i−i1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−iii−iζ7−ζ7ζ11−ζ11
χ2522222-12-1-1-12222-1-1-122-1-1-1222222220000-1-1-1-12222-1-1-1-122-1-1-1-100-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000
χ2622222-12-1-1-12−1−i3−1+i32-1-1-1−1−i3−1+i3-1-1-1−1−i3−1−i3−1+i3−1+i3222200001+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i3222-1-1-1-100-1-1-1-1−1−i3−1+i31+i321+i321+i321−i321−i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i320000000000000000
χ2722222-12-1-1-12−1+i3−1−i32-1-1-1−1+i3−1−i3-1-1-1−1+i3−1+i3−1−i3−1−i3222200001−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i3222-1-1-1-100-1-1-1-1−1+i3−1−i31−i321−i321−i321+i321+i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i320000000000000000
χ2822222-12-1-1-1-222-2-11122-111222222220000-1-1-1-12222-1-1-1-1-2-2-1-11100-1-111-2-2-111-111-2-2-111-1110000000000000000
χ2922222-12-1-1-1-2−1−i3−1+i3-2-111−1−i3−1+i3-111−1−i3−1−i3−1+i3−1+i3222200001+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i32-2-2-1-11100-1-1111+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i320000000000000000
χ3022222-12-1-1-1-2−1+i3−1−i3-2-111−1+i3−1−i3-111−1+i3−1+i3−1−i3−1−i3222200001−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i32-2-2-1-11100-1-1111−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i320000000000000000
χ312222-22-22220220-20022-2002222-222-200002222-2-2-2-2222200-2200002-20000-200-20000-200-2000000000000000000
χ322222-22-22220−1−i3−1+i30-200−1−i3−1+i3-200−1−i3−1−i3−1+i3−1+i3-222-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i300-2200002-200001+i3001−i300001+i3001−i3000000000000000000
χ332222-22-22220−1+i3−1−i30-200−1+i3−1−i3-200−1+i3−1+i3−1−i3−1−i3-222-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i300-2200002-200001−i3001+i300001−i3001+i3000000000000000000
χ342222-2-1-2-1-1-102201−i3i3221−i3i32222-222-20000-1-1-1-1-2-2-2-2-1-1-1-1001-1−i3i300-11−i3i3001−i3i31−i3i3001−i3i31−i3i30000000000000000
χ352222-2-1-2-1-1-102201i3−i3221i3−i32222-222-20000-1-1-1-1-2-2-2-2-1-1-1-1001-1i3−i300-11i3−i3001i3−i31i3−i3001i3−i31i3−i30000000000000000
χ362222-2-1-2-1-1-10−1−i3−1+i301−i3i3−1−i3−1+i31−i3i3−1−i3−1−i3−1+i3−1+i3-222-200001+i321−i321+i321−i321+i31−i31+i31−i31+i321+i321−i321−i32001-1−i3i300-11−i3i300−1−i32−3+i323−i32−1+i323+i32−3−i3200−1−i32−3+i323−i32−1+i323+i32−3−i320000000000000000
χ372222-2-1-2-1-1-10−1−i3−1+i301i3−i3−1−i3−1+i31i3−i3−1−i3−1−i3−1+i3−1+i3-222-200001+i321−i321+i321−i321+i31−i31+i31−i31+i321+i321−i321−i32001-1i3−i300-11i3−i300−1−i323−i32−3+i32−1+i32−3−i323+i3200−1−i323−i32−3+i32−1+i32−3−i323+i320000000000000000
χ382222-2-1-2-1-1-10−1+i3−1−i301−i3i3−1+i3−1−i31−i3i3−1+i3−1+i3−1−i3−1−i3-222-200001−i321+i321−i321+i321−i31+i31−i31+i31−i321−i321+i321+i32001-1−i3i300-11−i3i300−1+i323+i32−3−i32−1−i32−3+i323−i3200−1+i323+i32−3−i32−1−i32−3+i323−i320000000000000000
χ392222-2-1-2-1-1-10−1+i3−1−i301i3−i3−1+i3−1−i31i3−i3−1+i3−1+i3−1−i3−1−i3-222-200001−i321+i321−i321+i321−i31+i31−i31+i31−i321−i321+i321+i32001-1i3−i300-11i3−i300−1+i32−3−i323+i32−1−i323−i32−3+i3200−1+i32−3−i323+i32−1−i323−i32−3+i320000000000000000
χ4022-2-222-22-2-2022020022-200-2-2-2-2-2-2220000222222-2-2-2-2-2-200-2-2000022000020020000-200-2000000000000000000
χ4122-2-222-22-2-20−1−i3−1+i30200−1−i3−1+i3-2001+i31+i31−i31−i3-2-2220000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31−i31+i31+i31−i31−i300-2-20000220000−1−i300−1+i300001+i3001−i3000000000000000000
χ4222-2-222-22-2-20−1+i3−1−i30200−1+i3−1−i3-2001−i31−i31+i31+i3-2-2220000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31+i31−i31−i31+i31+i300-2-20000220000−1+i300−1−i300001−i3001+i3000000000000000000
χ4322-2-22-1-2-1110220-1−i3i3221i3−i3-2-2-2-2-2-2220000-1-1-1-122-2-211110011i3−i300-1-1−i3i300-1−i3i3-1−i3i3001i3−i31i3−i30000000000000000
χ4422-2-22-1-2-1110220-1i3−i3221−i3i3-2-2-2-2-2-2220000-1-1-1-122-2-211110011−i3i300-1-1i3−i300-1i3−i3-1i3−i3001−i3i31−i3i30000000000000000
χ4522-2-22-1-2-1110−1−i3−1+i30-1−i3i3−1−i3−1+i31i3−i31+i31+i31−i31−i3-2-22200001+i321−i321+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i320011i3−i300-1-1−i3i3001+i32−3+i323−i321−i323+i32−3−i3200−1−i323−i32−3+i32−1+i32−3−i323+i320000000000000000
χ4622-2-22-1-2-1110−1−i3−1+i30-1i3−i3−1−i3−1+i31−i3i31+i31+i31−i31−i3-2-22200001+i321−i321+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i320011−i3i300-1-1i3−i3001+i323−i32−3+i321−i32−3−i323+i3200−1−i32−3+i323−i32−1+i323+i32−3−i320000000000000000
χ4722-2-22-1-2-1110−1+i3−1−i30-1−i3i3−1+i3−1−i31i3−i31−i31−i31+i31+i3-2-22200001−i321+i321−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i320011i3−i300-1-1−i3i3001−i323+i32−3−i321+i32−3+i323−i3200−1+i32−3−i323+i32−1−i323−i32−3+i320000000000000000
χ4822-2-22-1-2-1110−1+i3−1−i30-1i3−i3−1+i3−1−i31−i3i31−i31−i31+i31+i3-2-22200001−i321+i321−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i320011−i3i300-1-1i3−i3001−i32−3−i323+i321+i323−i32−3+i3200−1+i323+i32−3−i32−1−i32−3+i323−i320000000000000000
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χ868-88i−8i0-404−4i4i02+2i32−2i30000−2−2i3−2+2i30004ζ11−4ζ114ζ7−4ζ700000000−1−i3−1+i31+i31−i30000−2ζ112ζ11−2ζ72ζ700000000000000000000000000000000000000000000
χ878-88i−8i0-404−4i4i02−2i32+2i30000−2+2i3−2−2i30004ζ7−4ζ74ζ11−4ζ1100000000−1+i3−1−i31−i31+i30000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000000000000000000
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χ908-8−8i8i0-4044i−4i02−2i32+2i30000−2+2i3−2−2i3000−4ζ74ζ7−4ζ114ζ1100000000−1+i3−1−i31−i31+i300002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.