Finite Group Databasebeta

← Group #13167100

Character table — Group #13167100

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122244444444488888888181824242424242424242436365454545472727211222444444444888888881818242424242424242424363654545454727272
order123463333666612361212121212128826666666624241616161641212226466666666612661212121212128826666666624241616161641212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ52222222222222222222222-2-2000000000-2-200000002222222222222222222222-2-2000000000-2-20000000
χ6222-2222222222-222-2-2-2-2-2-2000000000000022−2−2000222-2222222222-222-2-2-2-2-2-2000000000000022−2−2000
χ7222-2222222222-222-2-2-2-2-2-20000000000000−2−222000222-2222222222-222-2-2-2-2-2-20000000000000−2−222000
χ822-12-122-1-12-1-12-1-1-12-1-12-1-1222-1-122-1-1-1-1-1-1000000022-12-122-1-12-1-12-1-1-12-1-12-1-1222-1-122-1-1-1-1-1-10000000
χ922-12-122-1-12-1-12-1-1-12-1-12-1-122-211-2-21111-1-1000000022-12-122-1-12-1-12-1-1-12-1-12-1-122-211-2-21111-1-10000000
χ1022-12-122-1-12-1-12-1-1-12-1-12-1-1-2-20−i3i300−i3−i3i3i311000000022-12-122-1-12-1-12-1-1-12-1-12-1-1-2-20−i3i300−i3−i3i3i3110000000
χ1122-12-122-1-12-1-12-1-1-12-1-12-1-1-2-20i3−i300i3i3−i3−i311000000022-12-122-1-12-1-12-1-1-12-1-12-1-1-2-20i3−i300i3i3−i3−i3110000000
χ122-220-22222-2-2-2-202-20000002−20000000002−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430002-220-22222-2-2-2-202-20000002−20000000002−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000
χ132-220-22222-2-2-2-202-20000002−20000000002−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430002-220-22222-2-2-2-202-20000002−20000000002−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000
χ142-220-22222-2-2-2-202-2000000−22000000000−22ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470002-220-22222-2-2-2-202-2000000−22000000000−22ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000
χ152-220-22222-2-2-2-202-2000000−22000000000−22−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470002-220-22222-2-2-2-202-2000000−22000000000−22−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000
χ16444441-2-2-2-2-2-21411-2-2-2111000000000000000002-1-1444441-2-2-2-2-2-21411-2-2-2111000000000000000002-1-1
χ17444441-2-2-2-2-2-21411-2-2-211100000000000000000-211444441-2-2-2-2-2-21411-2-2-211100000000000000000-211
χ1844444-2111111-24-2-2111-2-2-200222-1-1-1-1-1-100000000044444-2111111-24-2-2111-2-2-200222-1-1-1-1-1-1000000000
χ1944444-2111111-24-2-2111-2-2-200-2-2-211111100000000044444-2111111-24-2-2111-2-2-200-2-2-2111111000000000
χ20444-441-2-2-2-2-2-21-411222-1-1-1000000000000000000−i3i3444-441-2-2-2-2-2-21-411222-1-1-1000000000000000000−i3i3
χ21444-441-2-2-2-2-2-21-411222-1-1-1000000000000000000i3−i3444-441-2-2-2-2-2-21-411222-1-1-1000000000000000000i3−i3
χ22444-44-2111111-2-4-2-2-1-1-122200000−i3i3−i3i3−i3i3000000000444-44-2111111-2-4-2-2-1-1-122200000−i3i3−i3i3−i3i3000000000
χ23444-44-2111111-2-4-2-2-1-1-122200000i3−i3i3−i3i3−i3000000000444-44-2111111-2-4-2-2-1-1-122200000i3−i3i3−i3i3−i3000000000
χ2444-24-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-211002−1−i3−1+i3-1-11+i321+i321−i321−i3200000000044-24-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-211002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000
χ2544-24-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-21100-21+i31−i311−1−i32−1−i32−1+i32−1+i3200000000044-24-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-21100-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000
χ2644-24-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-211002−1+i3−1−i3-1-11−i321−i321+i321+i3200000000044-24-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-211002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000
χ2744-24-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-21100-21−i31+i311−1+i32−1+i32−1−i32−1−i3200000000044-24-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-21100-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000
χ2844-2-4-244-2-24-2-242-2-2-422-4220000000000000000000044-2-4-244-2-24-2-242-2-2-422-42200000000000000000000
χ2944-2-4-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2211-11+3i321−3i322-1-100000−i3i3−3+i323−i323+i32−3−i3200000000044-2-4-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2211-11+3i321−3i322-1-100000−i3i3−3+i323−i323+i32−3−i32000000000
χ3044-2-4-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2211-11+3i321−3i322-1-100000i3−i33−i32−3+i32−3−i323+i3200000000044-2-4-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2211-11+3i321−3i322-1-100000i3−i33−i32−3+i32−3−i323+i32000000000
χ3144-2-4-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2211-11−3i321+3i322-1-100000−i3i33+i32−3−i32−3+i323−i3200000000044-2-4-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2211-11−3i321+3i322-1-100000−i3i33+i32−3−i32−3+i323−i32000000000
χ3244-2-4-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2211-11−3i321+3i322-1-100000i3−i3−3−i323+i323−i32−3+i3200000000044-2-4-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2211-11−3i321+3i322-1-100000i3−i3−3−i323+i323−i32−3+i32000000000
χ334-4-20244-2-2-422-40-2200000022−22000000000−2200000004-4-20244-2-2-422-40-2200000022−22000000000−220000000
χ344-4-20244-2-2-422-40-22000000−22220000000002−200000004-4-20244-2-2-422-40-22000000−22220000000002−20000000
χ3588-48-42-422-4222-4-1-1-4222-1-10000000000000000000088-48-42-422-4222-4-1-1-4222-1-100000000000000000000
χ3688-4-8-42-422-42224-1-14-2-2-2110000000000000000000088-4-8-42-422-42224-1-14-2-2-21100000000000000000000
χ378-880-82-4-4-4444-202-2000000000000000000000000008-880-82-4-4-4444-202-200000000000000000000000000
χ388-880-8-4222-2-2-240-44000000000000000000000000008-880-8-4222-2-2-240-4400000000000000000000000000
χ398-8-4042-4224-2-2-20-11000033−33000000000000000000008-8-4042-4224-2-2-20-11000033−3300000000000000000000
χ408-8-4042-4224-2-2-20-110000−3333000000000000000000008-8-4042-4224-2-2-20-110000−333300000000000000000000
χ418-8-404-42−1−3i3−1+3i3-21+3i31−3i3402-2000000000000000000000000008-8-404-42−1−3i3−1+3i3-21+3i31−3i3402-200000000000000000000000000
χ428-8-404-42−1+3i3−1−3i3-21−3i31+3i3402-2000000000000000000000000008-8-404-42−1+3i3−1−3i3-21−3i31+3i3402-200000000000000000000000000
χ43111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ45111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111
χ46111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1
χ472222222222222222222222-2-2000000000-2-20000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222000000000220000000
χ48222-2222222222-222-2-2-2-2-2-2000000000000022−2−2000-2-2-22-2-2-2-2-2-2-2-2-22-2-22222220000000000000−2−222000
χ49222-2222222222-222-2-2-2-2-2-20000000000000−2−222000-2-2-22-2-2-2-2-2-2-2-2-22-2-2222222000000000000022−2−2000
χ5022-12-122-1-12-1-12-1-1-12-1-12-1-1222-1-122-1-1-1-1-1-10000000-2-21-21-2-211-211-2111-211-211-2-2-211-2-21111110000000
χ5122-12-122-1-12-1-12-1-1-12-1-12-1-122-211-2-21111-1-10000000-2-21-21-2-211-211-2111-211-211-2-22-1-122-1-1-1-1110000000
χ5222-12-122-1-12-1-12-1-1-12-1-12-1-1-2-20−i3i300−i3−i3i3i3110000000-2-21-21-2-211-211-2111-211-211220i3−i300i3i3−i3−i3-1-10000000
χ5322-12-122-1-12-1-12-1-1-12-1-12-1-1-2-20i3−i300i3i3−i3−i3110000000-2-21-21-2-211-211-2111-211-211220−i3i300−i3−i3i3i3-1-10000000
χ542-220-22222-2-2-2-202-20000002−20000000002−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000-22-202-2-2-2-222220-22000000−22000000000−22ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000
χ552-220-22222-2-2-2-202-20000002−20000000002−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000-22-202-2-2-2-222220-22000000−22000000000−22−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000
χ562-220-22222-2-2-2-202-2000000−22000000000−22ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000-22-202-2-2-2-222220-220000002−20000000002−2−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000
χ572-220-22222-2-2-2-202-2000000−22000000000−22−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000-22-202-2-2-2-222220-220000002−20000000002−2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000
χ58444441-2-2-2-2-2-21411-2-2-2111000000000000000002-1-1-4-4-4-4-4-1222222-1-4-1-1222-1-1-100000000000000000-211
χ59444441-2-2-2-2-2-21411-2-2-211100000000000000000-211-4-4-4-4-4-1222222-1-4-1-1222-1-1-1000000000000000002-1-1
χ6044444-2111111-24-2-2111-2-2-200222-1-1-1-1-1-1000000000-4-4-4-4-42-1-1-1-1-1-12-422-1-1-122200-2-2-2111111000000000
χ6144444-2111111-24-2-2111-2-2-200-2-2-2111111000000000-4-4-4-4-42-1-1-1-1-1-12-422-1-1-122200222-1-1-1-1-1-1000000000
χ62444-441-2-2-2-2-2-21-411222-1-1-1000000000000000000−i3i3-4-4-44-4-1222222-14-1-1-2-2-2111000000000000000000i3−i3
χ63444-441-2-2-2-2-2-21-411222-1-1-1000000000000000000i3−i3-4-4-44-4-1222222-14-1-1-2-2-2111000000000000000000−i3i3
χ64444-44-2111111-2-4-2-2-1-1-122200000−i3i3−i3i3−i3i3000000000-4-4-44-42-1-1-1-1-1-12422111-2-2-200000i3−i3i3−i3i3−i3000000000
χ65444-44-2111111-2-4-2-2-1-1-122200000i3−i3i3−i3i3−i3000000000-4-4-44-42-1-1-1-1-1-12422111-2-2-200000−i3i3−i3i3−i3i3000000000
χ6644-24-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-211002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000-4-42-422-11+3i321−3i32-11+3i321−3i3222-1-1-11+3i321−3i322-1-100-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000
χ6744-24-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-21100-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000-4-42-422-11+3i321−3i32-11+3i321−3i3222-1-1-11+3i321−3i322-1-1002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000
χ6844-24-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-211002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000-4-42-422-11−3i321+3i32-11−3i321+3i3222-1-1-11−3i321+3i322-1-100-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000
χ6944-24-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-21100-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000-4-42-422-11−3i321+3i32-11−3i321+3i3222-1-1-11−3i321+3i322-1-1002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000
χ7044-2-4-244-2-24-2-242-2-2-422-42200000000000000000000-4-4242-4-422-422-4-2224-2-24-2-200000000000000000000
χ7144-2-4-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2211-11+3i321−3i322-1-100000−i3i3−3+i323−i323+i32−3−i32000000000-4-42422-11+3i321−3i32-11+3i321−3i322-2-1-11−1−3i32−1+3i32-21100000i3−i33−i32−3+i32−3−i323+i32000000000
χ7244-2-4-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2211-11+3i321−3i322-1-100000i3−i33−i32−3+i32−3−i323+i32000000000-4-42422-11+3i321−3i32-11+3i321−3i322-2-1-11−1−3i32−1+3i32-21100000−i3i3−3+i323−i323+i32−3−i32000000000
χ7344-2-4-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2211-11−3i321+3i322-1-100000−i3i33+i32−3−i32−3+i323−i32000000000-4-42422-11−3i321+3i32-11−3i321+3i322-2-1-11−1+3i32−1−3i32-21100000i3−i3−3−i323+i323−i32−3+i32000000000
χ7444-2-4-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2211-11−3i321+3i322-1-100000i3−i3−3−i323+i323−i32−3+i32000000000-4-42422-11−3i321+3i32-11−3i321+3i322-2-1-11−1+3i32−1−3i32-21100000−i3i33+i32−3−i32−3+i323−i32000000000
χ754-4-20244-2-2-422-40-2200000022−22000000000−220000000-4420-2-4-4224-2-2402-2000000−22220000000002−20000000
χ764-4-20244-2-2-422-40-22000000−22220000000002−20000000-4420-2-4-4224-2-2402-200000022−22000000000−220000000
χ7788-48-42-422-4222-4-1-1-4222-1-100000000000000000000-8-84-84-24-2-24-2-2-24114-2-2-21100000000000000000000
χ7888-4-8-42-422-42224-1-14-2-2-21100000000000000000000-8-8484-24-2-24-2-2-2-411-4222-1-100000000000000000000
χ798-880-82-4-4-4444-202-200000000000000000000000000-88-808-2444-4-4-420-2200000000000000000000000000
χ808-880-8-4222-2-2-240-4400000000000000000000000000-88-8084-2-2-2222-404-400000000000000000000000000
χ818-8-4042-4224-2-2-20-11000033−3300000000000000000000-8840-4-24-2-2-422201-10000−333300000000000000000000
χ828-8-4042-4224-2-2-20-110000−333300000000000000000000-8840-4-24-2-2-422201-1000033−3300000000000000000000
χ838-8-404-42−1−3i3−1+3i3-21+3i31−3i3402-200000000000000000000000000-8840-44-21+3i31−3i32−1−3i3−1+3i3-40-2200000000000000000000000000
χ848-8-404-42−1+3i3−1−3i3-21−3i31+3i3402-200000000000000000000000000-8840-44-21−3i31+3i32−1+3i3−1−3i3-40-2200000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.