Finite Group Databasebeta

← Group #13167098

Character table — Group #13167098

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122244444444488888888181824242424242424242436365454545472727211222444444444888888881818242424242424242424363654545454727272
order123463333666612361212121212128841212121212121212242416161616266226466666666612661212121212128841212121212121212242416161616266
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
χ822-12-12-1-1222-1-1-1-1-122-1-1-1-1222-1-122-1-1-1-1-1-1000000022-12-12-1-1222-1-1-1-1-122-1-1-1-1222-1-122-1-1-1-1-1-10000000
χ922-12-12-1-1222-1-1-1-1-122-1-1-1-122-211-2-21111-1-1000000022-12-12-1-1222-1-1-1-1-122-1-1-1-122-211-2-21111-1-10000000
χ1022-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-20−i3i300−i3−i3i3i311000000022-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-20−i3i300−i3−i3i3i3110000000
χ1122-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-20i3−i300i3i3−i3−i311000000022-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-20i3−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
χ1644444111-2-21114-2-2-2111-2-200222-1-1-1-1-1-100000000044444111-2-21114-2-2-2111-2-200222-1-1-1-1-1-1000000000
χ1744444111-2-21114-2-2-2111-2-200-2-2-211111100000000044444111-2-21114-2-2-2111-2-200-2-2-2111111000000000
χ1844444-2-2-211-2-2-24111-2-2-211000000000000000002-1-144444-2-2-211-2-2-24111-2-2-211000000000000000002-1-1
χ1944444-2-2-211-2-2-24111-2-2-21100000000000000000-21144444-2-2-211-2-2-24111-2-2-21100000000000000000-211
χ20444-44111-2-2111-4-2-22-1-1-12200000−i3i3−i3i3−i3i3000000000444-44111-2-2111-4-2-22-1-1-12200000−i3i3−i3i3−i3i3000000000
χ21444-44111-2-2111-4-2-22-1-1-12200000i3−i3i3−i3i3−i3000000000444-44111-2-2111-4-2-22-1-1-12200000i3−i3i3−i3i3−i3000000000
χ22444-44-2-2-211-2-2-2-411-1222-1-1000000000000000000−i3i3444-44-2-2-211-2-2-2-411-1222-1-1000000000000000000−i3i3
χ23444-44-2-2-211-2-2-2-411-1222-1-1000000000000000000i3−i3444-44-2-2-211-2-2-2-411-1222-1-1000000000000000000i3−i3
χ2444-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i3211002−1−i3−1+i3-1-11+i321+i321−i321−i3200000000044-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i3211002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000
χ2544-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i321100-21+i31−i311−1−i32−1−i32−1+i32−1+i3200000000044-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i321100-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000
χ2644-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i3211002−1+i3−1−i3-1-11−i321−i321+i321+i3200000000044-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i3211002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000
χ2744-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i321100-21−i31+i311−1+i32−1+i32−1−i32−1−i3200000000044-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i321100-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000
χ2844-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100000−i3i3−3+i323−i323+i32−3−i3200000000044-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100000−i3i3−3+i323−i323+i32−3−i32000000000
χ2944-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100000i3−i33−i32−3+i32−3−i323+i3200000000044-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100000i3−i33−i32−3+i32−3−i323+i32000000000
χ3044-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100000−i3i33+i32−3−i32−3+i323−i3200000000044-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100000−i3i33+i32−3−i32−3+i323−i32000000000
χ3144-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100000i3−i3−3−i323+i323−i32−3+i3200000000044-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100000i3−i3−3−i323+i323−i32−3+i32000000000
χ3244-2-4-24-2-2444-2-22-2-2-4-422220000000000000000000044-2-4-24-2-2444-2-22-2-2-4-4222200000000000000000000
χ334-4-2024-2-24-4-4220-2200000022−22000000000−2200000004-4-2024-2-24-4-4220-2200000022−22000000000−220000000
χ344-4-2024-2-24-4-4220-22000000−22220000000002−200000004-4-2024-2-24-4-4220-22000000−22220000000002−20000000
χ3588-48-4-42222-422-4-1-12-422-1-10000000000000000000088-48-4-42222-422-4-1-12-422-1-100000000000000000000
χ3688-4-8-4-42222-4224-1-1-24-2-2110000000000000000000088-4-8-4-42222-4224-1-1-24-2-21100000000000000000000
χ378-880-8222-44-2-2-20-44000000000000000000000000008-880-8222-44-2-2-20-4400000000000000000000000000
χ388-880-8-4-4-42-244402-2000000000000000000000000008-880-8-4-4-42-244402-200000000000000000000000000
χ398-8-4042−1−3i3−1+3i3-44-21+3i31−3i302-2000000000000000000000000008-8-4042−1−3i3−1+3i3-44-21+3i31−3i302-200000000000000000000000000
χ408-8-4042−1+3i3−1−3i3-44-21−3i31+3i302-2000000000000000000000000008-8-4042−1+3i3−1−3i3-44-21−3i31+3i302-200000000000000000000000000
χ418-8-404-4222-24-2-20-11000033−33000000000000000000008-8-404-4222-24-2-20-11000033−3300000000000000000000
χ428-8-404-4222-24-2-20-110000−3333000000000000000000008-8-404-4222-24-2-20-110000−333300000000000000000000
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
χ5022-12-12-1-1222-1-1-1-1-122-1-1-1-1222-1-122-1-1-1-1-1-10000000-2-21-21-211-2-2-211111-2-21111-2-2-211-2-21111110000000
χ5122-12-12-1-1222-1-1-1-1-122-1-1-1-122-211-2-21111-1-10000000-2-21-21-211-2-2-211111-2-21111-2-22-1-122-1-1-1-1110000000
χ5222-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-20−i3i300−i3−i3i3i3110000000-2-21-21-211-2-2-211111-2-21111220i3−i300i3i3−i3−i3-1-10000000
χ5322-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-20i3−i300i3i3−i3−i3110000000-2-21-21-211-2-2-211111-2-21111220−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
χ5844444111-2-21114-2-2-2111-2-200222-1-1-1-1-1-1000000000-4-4-4-4-4-1-1-122-1-1-1-4222-1-1-12200-2-2-2111111000000000
χ5944444111-2-21114-2-2-2111-2-200-2-2-2111111000000000-4-4-4-4-4-1-1-122-1-1-1-4222-1-1-12200222-1-1-1-1-1-1000000000
χ6044444-2-2-211-2-2-24111-2-2-211000000000000000002-1-1-4-4-4-4-4222-1-1222-4-1-1-1222-1-100000000000000000-211
χ6144444-2-2-211-2-2-24111-2-2-21100000000000000000-211-4-4-4-4-4222-1-1222-4-1-1-1222-1-1000000000000000002-1-1
χ62444-44111-2-2111-4-2-22-1-1-12200000−i3i3−i3i3−i3i3000000000-4-4-44-4-1-1-122-1-1-1422-2111-2-200000i3−i3i3−i3i3−i3000000000
χ63444-44111-2-2111-4-2-22-1-1-12200000i3−i3i3−i3i3−i3000000000-4-4-44-4-1-1-122-1-1-1422-2111-2-200000−i3i3−i3i3−i3i3000000000
χ64444-44-2-2-211-2-2-2-411-1222-1-1000000000000000000−i3i3-4-4-44-4222-1-12224-1-11-2-2-211000000000000000000i3−i3
χ65444-44-2-2-211-2-2-2-411-1222-1-1000000000000000000i3−i3-4-4-44-4222-1-12224-1-11-2-2-211000000000000000000−i3i3
χ6644-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i3211002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000-4-42-42-11+3i321−3i3222-11+3i321−3i322-1-12-11+3i321−3i32-1-100-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000
χ6744-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i321100-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000-4-42-42-11+3i321−3i3222-11+3i321−3i322-1-12-11+3i321−3i32-1-1002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000
χ6844-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i3211002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000-4-42-42-11−3i321+3i3222-11−3i321+3i322-1-12-11−3i321+3i32-1-100-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000
χ6944-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i321100-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000-4-42-42-11−3i321+3i3222-11−3i321+3i322-1-12-11−3i321+3i32-1-1002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000
χ7044-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100000−i3i3−3+i323−i323+i32−3−i32000000000-4-4242-11+3i321−3i3222-11+3i321−3i32-2-1-1-21−1−3i32−1+3i321100000i3−i33−i32−3+i32−3−i323+i32000000000
χ7144-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100000i3−i33−i32−3+i32−3−i323+i32000000000-4-4242-11+3i321−3i3222-11+3i321−3i32-2-1-1-21−1−3i32−1+3i321100000−i3i3−3+i323−i323+i32−3−i32000000000
χ7244-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100000−i3i33+i32−3−i32−3+i323−i32000000000-4-4242-11−3i321+3i3222-11−3i321+3i32-2-1-1-21−1+3i32−1−3i321100000i3−i3−3−i323+i323−i32−3+i32000000000
χ7344-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100000i3−i3−3−i323+i323−i32−3+i32000000000-4-4242-11−3i321+3i3222-11−3i321+3i32-2-1-1-21−1+3i32−1−3i321100000−i3i33+i32−3−i32−3+i323−i32000000000
χ7444-2-4-24-2-2444-2-22-2-2-4-4222200000000000000000000-4-4242-422-4-4-422-22244-2-2-2-200000000000000000000
χ754-4-2024-2-24-4-4220-2200000022−22000000000−220000000-4420-2-422-444-2-202-2000000−22220000000002−20000000
χ764-4-2024-2-24-4-4220-22000000−22220000000002−20000000-4420-2-422-444-2-202-200000022−22000000000−220000000
χ7788-48-4-42222-422-4-1-12-422-1-100000000000000000000-8-84-844-2-2-2-24-2-2411-24-2-21100000000000000000000
χ7888-4-8-4-42222-4224-1-1-24-2-21100000000000000000000-8-84844-2-2-2-24-2-2-4112-422-1-100000000000000000000
χ798-880-8222-44-2-2-20-4400000000000000000000000000-88-808-2-2-24-422204-400000000000000000000000000
χ808-880-8-4-4-42-244402-200000000000000000000000000-88-808444-22-4-4-40-2200000000000000000000000000
χ818-8-4042−1−3i3−1+3i3-44-21+3i31−3i302-200000000000000000000000000-8840-4-21+3i31−3i34-42−1−3i3−1+3i30-2200000000000000000000000000
χ828-8-4042−1+3i3−1−3i3-44-21−3i31+3i302-200000000000000000000000000-8840-4-21−3i31+3i34-42−1+3i3−1−3i30-2200000000000000000000000000
χ838-8-404-4222-24-2-20-11000033−3300000000000000000000-8840-44-2-2-22-42201-10000−333300000000000000000000
χ848-8-404-4222-24-2-20-110000−333300000000000000000000-8840-44-2-2-22-42201-1000033−3300000000000000000000

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