Finite Group Databasebeta

← Group #11921379

Character table — Group #11921379

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444444666666668888888888881212121212121212121212121616161616161616161616161616161624242424242424243636363648484848
order1222344666223366666666661212224488883366666612121212444466121212121212666666666666121212122424242424242424448812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−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
χ4111111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111111111−1−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
χ5111111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+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
χ6111111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111111111−1+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
χ71111111111-1-111-1-1-1-11111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1
χ81111111111-1-111-1-1-1-1111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ91111111111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-11+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1111+i321+i321−i321−i32
χ101111111111-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-11111-1-1-1-11+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i32
χ111111111111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-11−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1111−i321−i321+i321+i32
χ121111111111-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-11111-1-1-1-11−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i32
χ131-11-111-1-1-111-11111-1-1-1-111-1-11-11-11-1ii−i−i11-1-1-1-11111-1-1i−i1-11-11-111-1-11-11-111-1-111-1-11-11-1ii−i−iii−i−ii−ii−ii−ii−i
χ141-11-111-1-1-111-11111-1-1-1-111-1-11-11-11-1−i−iii11-1-1-1-11111-1-1−ii1-11-11-111-1-11-11-111-1-111-1-11-11-1−i−iii−i−iii−ii−ii−ii−ii
χ151-11-111-1-1-111-1−1−i32−1+i3211-1-11+i321−i32−1−i32−1+i321+i321−i321-11-11-1ii−i−i−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32i−i1-11-11-111-1-1−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14i−ii−iζ22−ζ22ζ14−ζ14
χ161-11-111-1-1-111-1−1−i32−1+i3211-1-11+i321−i32−1−i32−1+i321+i321−i321-11-11-1−i−iii−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−ii1-11-11-111-1-1−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ii−ii−ζ22ζ22−ζ14ζ14
χ171-11-111-1-1-111-1−1+i32−1−i3211-1-11−i321+i32−1+i32−1−i321−i321+i321-11-11-1ii−i−i−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32i−i1-11-11-111-1-1−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22i−ii−iζ14−ζ14ζ22−ζ22
χ181-11-111-1-1-111-1−1+i32−1−i3211-1-11−i321+i32−1+i32−1−i321−i321+i321-11-11-1−i−iii−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32−ii1-11-11-111-1-1−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ii−ii−ζ14ζ14−ζ22ζ22
χ191-11-111-1-1-11-1111-1-111-1-111-1-11-11-11-1ii−i−i11-1-1-1-11111-1-1−ii-111-11-1-1-111-11-11-1-111-1-1111-11-1ii−i−iii−i−i−iii−i−ii−ii
χ201-11-111-1-1-11-1111-1-111-1-111-1-11-11-11-1−i−iii11-1-1-1-11111-1-1i−i-111-11-1-1-111-11-11-1-111-1-1111-11-1−i−iii−i−iiii−i−iii−ii−i
χ211-11-111-1-1-11-11−1−i32−1+i32-1-1111+i321−i32−1−i32−1+i321+i321−i321-11-11-1ii−i−i−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−ii-111-11-1-1-1111+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14−iii−i−ζ22ζ22−ζ14ζ14
χ221-11-111-1-1-11-11−1−i32−1+i32-1-1111+i321−i32−1−i32−1+i321+i321−i321-11-11-1−i−iii−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32i−i-111-11-1-1-1111+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14i−i−iiζ22−ζ22ζ14−ζ14
χ231-11-111-1-1-11-11−1+i32−1−i32-1-1111−i321+i32−1+i32−1−i321−i321+i321-11-11-1ii−i−i−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32−ii-111-11-1-1-1111−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22−iii−i−ζ14ζ14−ζ22ζ22
χ241-11-111-1-1-11-11−1+i32−1−i32-1-1111−i321+i32−1+i32−1−i321−i321+i321-11-11-1−i−iii−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32i−i-111-11-1-1-1111−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22i−i−iiζ14−ζ14ζ22−ζ22
χ2522222-2-222200220000222222-2-2-2-222000022222222-2-2-2-20000-2-2220000000000000000-2-2-2-20000000000000000
χ2622222-2-222200−1−i3−1+i30000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-2-2-2220000−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000-2-22200000000000000001+i31+i31−i31−i30000000000000000
χ2722222-2-222200−1+i3−1−i30000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-2-2-2220000−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000-2-22200000000000000001−i31−i31+i31+i30000000000000000
χ282222-122-1-1-12222-1-1-1-1222222-1-122220000-1-1-1-1-1-1-1-122220022-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ292222-122-1-1-122−1−i3−1+i3-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1222200001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i30022-1-1-1-1-1-1-1-1−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i320000000000000000
χ302222-122-1-1-122−1+i3−1−i3-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1222200001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i30022-1-1-1-1-1-1-1-1−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i320000000000000000
χ312222-122-1-1-1-2-2221111222222-1-122220000-1-1-1-1-1-1-1-1222200-2-2-1-1-1-11111-2-2-2-211111111-1-1-1-10000000000000000
χ322222-122-1-1-1-2-2−1−i3−1+i31111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1222200001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i300-2-2-1-1-1-111111+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i320000000000000000
χ332222-122-1-1-1-2-2−1+i3−1−i31111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1222200001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i300-2-2-1-1-1-111111−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i320000000000000000
χ342222-1-2-2-1-1-10022−i3i3−i3i322222211-2-2220000-1-1-1-1-1-1-1-1-2-2-2-2000011-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i311110000000000000000
χ352222-1-2-2-1-1-10022i3−i3i3−i322222211-2-2220000-1-1-1-1-1-1-1-1-2-2-2-2000011-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i311110000000000000000
χ362222-1-2-2-1-1-100−1−i3−1+i3−i3i3−i3i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-2-22200001+i321−i321+i321+i321−i321−i321+i321−i321+i31−i31+i31−i3000011-1-1−i3i3−i3i30000−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i32−1−i32−1−i32−1+i32−1+i320000000000000000
χ372222-1-2-2-1-1-100−1−i3−1+i3i3−i3i3−i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-2-22200001+i321−i321+i321+i321−i321−i321+i321−i321+i31−i31+i31−i3000011-1-1i3−i3i3−i300003−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i32−1−i32−1−i32−1+i32−1+i320000000000000000
χ382222-1-2-2-1-1-100−1+i3−1−i3−i3i3−i3i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-2-22200001−i321+i321−i321−i321+i321+i321−i321+i321−i31+i31−i31+i3000011-1-1−i3i3−i3i300003+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i32−1+i32−1+i32−1−i32−1−i320000000000000000
χ392222-1-2-2-1-1-100−1+i3−1−i3i3−i3i3−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-2-22200001−i321+i321−i321−i321+i321+i321−i321+i321−i31+i31−i31+i3000011-1-1i3−i3i3−i30000−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i32−1+i32−1+i32−1−i32−1−i320000000000000000
χ402-22-22-22-2-2200220000-2-222-2-2-22-222-2000022-2-2-2-222-2-2220000-222-20000000000000000-22-220000000000000000
χ412-22-22-22-2-2200−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i3-22-222-20000−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i30000-222-200000000000000001+i3−1−i31−i3−1+i30000000000000000
χ422-22-22-22-2-2200−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i3-22-222-20000−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i30000-222-200000000000000001−i3−1+i31+i3−1−i30000000000000000
χ432-22-2-12-211-12-222-1-111-2-222-2-2-112-22-20000-1-11111-1-122-2-2002-2-11-11-1-1112-22-2-1-111-1-111-11-110000000000000000
χ442-22-2-12-211-12-2−1−i3−1+i3-1-1111+i31−i3−1−i3−1+i31+i31−i3-112-22-200001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i3−1+i31+i31−i3002-2-11-11-1-111−1−i31+i3−1+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i320000000000000000
χ452-22-2-12-211-12-2−1+i3−1−i3-1-1111−i31+i3−1+i3−1−i31−i31+i3-112-22-200001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i3−1−i31−i31+i3002-2-11-11-1-111−1+i31−i3−1−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i320000000000000000
χ462-22-2-12-211-1-222211-1-1-2-222-2-2-112-22-20000-1-11111-1-122-2-200-22-11-1111-1-1-22-2211-1-111-1-1-11-110000000000000000
χ472-22-2-12-211-1-22−1−i3−1+i311-1-11+i31−i3−1−i3−1+i31+i31−i3-112-22-200001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i3−1+i31+i31−i300-22-11-1111-1-11+i3−1−i31−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321−i32−1+i320000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.