Finite Group Databasebeta

← Group #72259826

Character table — Group #72259826

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112889916182424242448484848545472727272727210810810810810814414411288991618242424244848484854547272727272721081081081081081441441128899161824242424484848485454727272727272108108108108108144144
order124362212436121236121244226612124888866361236661212361212361212121266661212122424242466361236661212361212361212121266661212122424242466
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-111111-1-1-1-1-1-11111111111111111111-1-111111-1-1-1-1-1-11111111111111111111-1-111111-1-1-1-1-1-1
χ311-11111-1-111-1-111-1-1111-111-1-1-111-1-11-111-11111-1-111-1-111-1-1111-111-1-1-111-1-11-111-11111-1-111-1-111-1-1111-111-1-1-111-1-11-1
χ411-11111-1-111-1-111-1-111-1111-1-1-1-1-111-1111-11111-1-111-1-111-1-111-1111-1-1-1-1-111-1111-11111-1-111-1-111-1-111-1111-1-1-1-1-111-11
χ5222222222-1-1-1-1-1-1-1-12200-1-1-1-12000000222222222-1-1-1-1-1-1-1-12200-1-1-1-12000000222222222-1-1-1-1-1-1-1-12200-1-1-1-12000000
χ622222-2-22-2-1-1-1-1-1-1-1-1000011110−i2i2−i2i20022222-2-22-2-1-1-1-1-1-1-1-1000011110−i2i2−i2i20022222-2-22-2-1-1-1-1-1-1-1-1000011110−i2i2−i2i200
χ722222-2-22-2-1-1-1-1-1-1-1-1000011110i2−i2i2−i20022222-2-22-2-1-1-1-1-1-1-1-1000011110i2−i2i2−i20022222-2-22-2-1-1-1-1-1-1-1-1000011110i2−i2i2−i200
χ822-22222-2-2-1-111-1-1112200-1-111-200000022-22222-2-2-1-111-1-1112200-1-111-200000022-22222-2-2-1-111-1-1112200-1-111-2000000
χ922-222-2-2-22-1-111-1-111000011-1-10−i2i2i2−i20022-222-2-2-22-1-111-1-111000011-1-10−i2i2i2−i20022-222-2-2-22-1-111-1-111000011-1-10−i2i2i2−i200
χ1022-222-2-2-22-1-111-1-111000011-1-10i2−i2−i2i20022-222-2-2-22-1-111-1-111000011-1-10i2−i2−i2i20022-222-2-2-22-1-111-1-111000011-1-10i2−i2−i2i200
χ112-202-22-2002-2002-200-22002-20000000002-202-22-2002-2002-200-22002-20000000002-202-22-2002-2002-200-22002-2000000000
χ122-202-22-200-113−3-113−3-2200-113−300000002-202-22-200-113−3-113−3-2200-113−300000002-202-22-200-113−3-113−3-2200-113−30000000
χ132-202-22-200-11−33-11−33-2200-11−3300000002-202-22-200-11−33-11−33-2200-11−3300000002-202-22-200-11−33-11−33-2200-11−330000000
χ1433333333300000000-1-1110000-1-1-1-1-11133333333300000000-1-1110000-1-1-1-1-11133333333300000000-1-1110000-1-1-1-1-111
χ1533333333300000000-1-1-1-10000-11111-1-133333333300000000-1-1-1-10000-11111-1-133333333300000000-1-1-1-10000-11111-1-1
χ1633-33333-3-300000000-1-11-100001-1-1111-133-33333-3-300000000-1-11-100001-1-1111-133-33333-3-300000000-1-11-100001-1-1111-1
χ1733-33333-3-300000000-1-1-110000111-1-1-1133-33333-3-300000000-1-1-110000111-1-1-1133-33333-3-300000000-1-1-110000111-1-1-11
χ1844444-4-44-4111111110000-1-1-1-1000000044444-4-44-4111111110000-1-1-1-1000000044444-4-44-4111111110000-1-1-1-10000000
χ1944-444-4-4-4411-1-111-1-10000-1-111000000044-444-4-4-4411-1-111-1-10000-1-111000000044-444-4-4-4411-1-111-1-10000-1-1110000000
χ204-404-4-44001-13−31-13−30000-11−3300000004-404-4-44001-13−31-13−30000-11−3300000004-404-4-44001-13−31-13−30000-11−330000000
χ214-404-4-44001-1−331-1−330000-113−300000004-404-4-44001-1−331-1−330000-113−300000004-404-4-44001-1−331-1−330000-113−30000000
χ224-404-4-4400-2200-220000002-20000000004-404-4-4400-2200-220000002-20000000004-404-4-4400-2200-220000002-2000000000
χ236-606-66-600000000002-200000000000006-606-66-600000000002-200000000000006-606-66-600000000002-20000000000000
χ24888-1-100-102222-1-1-1-10022000000000-1-1888-1-100-102222-1-1-1-10022000000000-1-1888-1-100-102222-1-1-1-10022000000000-1-1
χ25888-1-100-102222-1-1-1-100-2-200000000011888-1-100-102222-1-1-1-100-2-200000000011888-1-100-102222-1-1-1-100-2-200000000011
χ2688-8-1-1001022-2-2-1-111002-2000000000-1188-8-1-1001022-2-2-1-111002-2000000000-1188-8-1-1001022-2-2-1-111002-2000000000-11
χ2788-8-1-1001022-2-2-1-11100-220000000001-188-8-1-1001022-2-2-1-11100-220000000001-188-8-1-1001022-2-2-1-11100-220000000001-1
χ28161616-2-200-20-2-2-2-21111000000000000000161616-2-200-20-2-2-2-21111000000000000000161616-2-200-20-2-2-2-21111000000000000000
χ291616-16-2-20020-2-22211-1-10000000000000001616-16-2-20020-2-22211-1-10000000000000001616-16-2-20020-2-22211-1-1000000000000000
χ3016-160-2200004-400-220000000000000000016-160-2200004-400-220000000000000000016-160-2200004-400-2200000000000000000
χ3116-160-220000-2223−231-1−3300000000000000016-160-220000-2223−231-1−3300000000000000016-160-220000-2223−231-1−33000000000000000
χ3216-160-220000-22−23231-13−300000000000000016-160-220000-22−23231-13−300000000000000016-160-220000-22−23231-13−3000000000000000
χ3311111111111111111111111111111111−1+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+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−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
χ341111111111111111111-1-111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ3511-11111-1-111-1-111-1-1111-111-1-1-111-1-11-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ3611-11111-1-111-1-111-1-111-1111-1-1-1-1-111-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ37222222222-1-1-1-1-1-1-1-12200-1-1-1-12000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3001−i321−i321−i321−i32−1+i3000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3001+i321+i321+i321+i32−1−i3000000
χ3822222-2-22-2-1-1-1-1-1-1-1-1000011110−i2i2−i2i200−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i321−i321−i321−i321−i321−i321−i321−i320000−1+i32−1+i32−1+i32−1+i320ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i321+i321+i321+i321+i321+i321+i321+i320000−1−i32−1−i32−1−i32−1−i320ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1300
χ3922222-2-22-2-1-1-1-1-1-1-1-1000011110i2−i2i2−i200−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i321−i321−i321−i321−i321−i321−i321−i320000−1+i32−1+i32−1+i32−1+i320−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i321+i321+i321+i321+i321+i321+i321+i320000−1−i32−1−i32−1−i32−1−i320−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ1300
χ4022-22222-2-2-1-111-1-1112200-1-111-2000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i3−1+i3001−i321−i32−1+i32−1+i321−i3000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i3−1−i3001+i321+i32−1−i32−1−i321+i3000000
χ4122-222-2-2-22-1-111-1-111000011-1-10−i2i2i2−i200−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3−1+i31−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i320000−1+i32−1+i321−i321−i320ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3−1−i31+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i320000−1−i32−1−i321+i321+i320ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1300
χ4222-222-2-2-22-1-111-1-111000011-1-10i2−i2−i2i200−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3−1+i31−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i320000−1+i32−1+i321−i321−i320−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3−1−i31+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i320000−1−i32−1−i321+i321+i320−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ1300
χ432-202-22-2002-2002-200-22002-2000000000−1+i31−i30−1+i31−i3−1+i31−i300−1+i31−i300−1+i31−i3001−i3−1+i300−1+i31−i3000000000−1−i31+i30−1−i31+i3−1−i31+i300−1−i31+i300−1−i31+i3001+i3−1−i300−1−i31+i3000000000
χ442-202-22-200-113−3-113−3-2200-113−30000000−1+i31−i30−1+i31−i3−1+i31−i3001−i32−1+i32−ζ14−2ζ22ζ14+2ζ221−i32−1+i32−ζ14−2ζ22ζ14+2ζ221−i3−1+i3001−i32−1+i32−ζ14−2ζ22ζ14+2ζ220000000−1−i31+i30−1−i31+i3−1−i31+i3001+i32−1−i322ζ14+ζ22−2ζ14−ζ221+i32−1−i322ζ14+ζ22−2ζ14−ζ221+i3−1−i3001+i32−1−i322ζ14+ζ22−2ζ14−ζ220000000
χ452-202-22-200-11−33-11−33-2200-11−330000000−1+i31−i30−1+i31−i3−1+i31−i3001−i32−1+i32ζ14+2ζ22−ζ14−2ζ221−i32−1+i32ζ14+2ζ22−ζ14−2ζ221−i3−1+i3001−i32−1+i32ζ14+2ζ22−ζ14−2ζ220000000−1−i31+i30−1−i31+i3−1−i31+i3001+i32−1−i32−2ζ14−ζ222ζ14+ζ221+i32−1−i32−2ζ14−ζ222ζ14+ζ221+i3−1−i3001+i32−1−i32−2ζ14−ζ222ζ14+ζ220000000
χ4633333333300000000-1-1110000-1-1-1-1-111−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32000000001−i321−i32−1+i32−1+i3200001−i321−i321−i321−i321−i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32000000001+i321+i32−1−i32−1−i3200001+i321+i321+i321+i321+i32−1−i32−1−i32
χ4733333333300000000-1-1-1-10000-11111-1-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32000000001−i321−i321−i321−i3200001−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32000000001+i321+i321+i321+i3200001+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ4833-33333-3-300000000-1-11-100001-1-1111-1−3+3i32−3+3i323−3i32−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i32000000001−i321−i32−1+i321−i320000−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−3−3i32−3−3i323+3i32−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i32000000001+i321+i32−1−i321+i320000−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ4933-33333-3-300000000-1-1-110000111-1-1-11−3+3i32−3+3i323−3i32−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i32000000001−i321−i321−i32−1+i320000−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−3−3i32−3−3i323+3i32−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i32000000001+i321+i321+i32−1−i320000−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ5044444-4-44-4111111110000-1-1-1-10000000−2+2i3−2+2i3−2+2i3−2+2i3−2+2i32−2i32−2i3−2+2i32−2i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200001−i321−i321−i321−i320000000−2−2i3−2−2i3−2−2i3−2−2i3−2−2i32+2i32+2i3−2−2i32+2i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3200001+i321+i321+i321+i320000000
χ5144-444-4-4-4411-1-111-1-10000-1-1110000000−2+2i3−2+2i32−2i3−2+2i3−2+2i32−2i32−2i32−2i3−2+2i3−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i3200001−i321−i32−1+i32−1+i320000000−2−2i3−2−2i32+2i3−2−2i3−2−2i32+2i32+2i32+2i3−2−2i3−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i3200001+i321+i32−1−i32−1−i320000000
χ524-404-4-44001-13−31-13−30000-11−330000000−2+2i32−2i30−2+2i32−2i32−2i3−2+2i300−1+i321−i32−ζ14−2ζ22ζ14+2ζ22−1+i321−i32−ζ14−2ζ22ζ14+2ζ2200001−i32−1+i32ζ14+2ζ22−ζ14−2ζ220000000−2−2i32+2i30−2−2i32+2i32+2i3−2−2i300−1−i321+i322ζ14+ζ22−2ζ14−ζ22−1−i321+i322ζ14+ζ22−2ζ14−ζ2200001+i32−1−i32−2ζ14−ζ222ζ14+ζ220000000
χ534-404-4-44001-1−331-1−330000-113−30000000−2+2i32−2i30−2+2i32−2i32−2i3−2+2i300−1+i321−i32ζ14+2ζ22−ζ14−2ζ22−1+i321−i32ζ14+2ζ22−ζ14−2ζ2200001−i32−1+i32−ζ14−2ζ22ζ14+2ζ220000000−2−2i32+2i30−2−2i32+2i32+2i3−2−2i300−1−i321+i32−2ζ14−ζ222ζ14+ζ22−1−i321+i32−2ζ14−ζ222ζ14+ζ2200001+i32−1−i322ζ14+ζ22−2ζ14−ζ220000000
χ544-404-4-4400-2200-220000002-2000000000−2+2i32−2i30−2+2i32−2i32−2i3−2+2i3001−i3−1+i3001−i3−1+i3000000−1+i31−i3000000000−2−2i32+2i30−2−2i32+2i32+2i3−2−2i3001+i3−1−i3001+i3−1−i3000000−1−i31+i3000000000
χ556-606-66-600000000002-20000000000000−3+3i33−3i30−3+3i33−3i3−3+3i33−3i30000000000−1+i31−i30000000000000−3−3i33+3i30−3−3i33+3i3−3−3i33+3i30000000000−1−i31+i30000000000000
χ56888-1-100-102222-1-1-1-10022000000000-1-1−4+4i3−4+4i3−4+4i31−i321−i32001−i320−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i3200−1+i3−1+i30000000001−i321−i32−4−4i3−4−4i3−4−4i31+i321+i32001+i320−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i3200−1−i3−1−i30000000001+i321+i32
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χ9416-160-2200004-400-2200000000000000000−8−8i38+8i301+i3−1−i30000−2−2i32+2i3001+i3−1−i300000000000000000−8+8i38−8i301−i3−1+i30000−2+2i32−2i3001−i3−1+i300000000000000000
χ9516-160-220000-2223−231-1−33000000000000000−8−8i38+8i301+i3−1−i300001+i3−1−i34ζ14+2ζ22−4ζ14−2ζ22−1−i321+i32−2ζ14−ζ222ζ14+ζ22000000000000000−8+8i38−8i301−i3−1+i300001−i3−1+i3−2ζ14−4ζ222ζ14+4ζ22−1+i321−i32ζ14+2ζ22−ζ14−2ζ22000000000000000
χ9616-160-220000-22−23231-13−3000000000000000−8−8i38+8i301+i3−1−i300001+i3−1−i3−4ζ14−2ζ224ζ14+2ζ22−1−i321+i322ζ14+ζ22−2ζ14−ζ22000000000000000−8+8i38−8i301−i3−1+i300001−i3−1+i32ζ14+4ζ22−2ζ14−4ζ22−1+i321−i32−ζ14−2ζ22ζ14+2ζ22000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.