Finite Group Databasebeta

← Group #13167282

Character table — Group #13167282

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122224444444444444444444888888888888888812121212121212121212121218181818181818182424242424242424242424243636727272727272108108108108
order1222366623333666666666666663666666666666666444412121212121212124444121212121212121212121212121212121212246612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111-11111-1-11111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111-111-1-111-1-1
χ611111111-11111-1-11111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-11-1-111-1-111
χ711111111-11111-1-11111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-111
χ811111111-11111-1-11111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-1
χ92222222222222222222222222222222222222222222000000000000-2-2-2-2-2-2-2-2000000000000-2-20000000000
χ1022222222-22222-2-22222222222222-2-2-2-2-2-2-2-2222-2-2-2-200000000000022-2-22222000000000000-2-20000000000
χ112222-1-1-1-122-1-12-1-12-1-12222-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-2-2-2-2111100−i3−i3i3i300−i3−i3i3i3110000000000
χ122222-1-1-1-122-1-12-1-12-1-12222-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-2-2-2-2111100i3i3−i3−i300i3i3−i3−i3110000000000
χ132222-1-1-1-122-1-12-1-12-1-12222-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-10000000000
χ142222-1-1-1-122-1-12-1-12-1-12222-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-21111-2-21111-1-10000000000
χ152222-1-1-1-1-22-1-12112-1-12222-1-1-1-12-1-2-21111-2-2-1-1-111110000−i3−i3i3i3i3i3−i3−i322-2-2-1-1-1-100−i3−i3i3i300i3i3−i3−i3110000000000
χ162222-1-1-1-1-22-1-12112-1-12222-1-1-1-12-1-2-21111-2-2-1-1-111110000i3i3−i3−i3−i3−i3i3i322-2-2-1-1-1-100i3i3−i3−i300−i3−i3i3i3110000000000
χ172222-1-1-1-1-22-1-12112-1-12222-1-1-1-12-1-2-21111-2-2-1-1-1111122-2-2-1-1-1-11111-2-222111122-1-1-1-1-2-21111-1-10000000000
χ182222-1-1-1-1-22-1-12112-1-12222-1-1-1-12-1-2-21111-2-2-1-1-11111-2-2221111-1-1-1-1-2-2221111-2-2111122-1-1-1-1-1-10000000000
χ1922-2-222-2-20222200-2-2-22-22-222-2-2-22000000002-2-200000000000000002i−2i002i2i−2i−2i000000000000000000002−2−i2i2
χ2022-2-222-2-20222200-2-2-22-22-222-2-2-22000000002-2-200000000000000002i−2i002i2i−2i−2i00000000000000000000−22i2−i2
χ2122-2-222-2-20222200-2-2-22-22-222-2-2-22000000002-2-20000000000000000−2i2i00−2i−2i2i2i000000000000000000002−2i2−i2
χ2222-2-222-2-20222200-2-2-22-22-222-2-2-22000000002-2-20000000000000000−2i2i00−2i−2i2i2i00000000000000000000−22−i2i2
χ232-22-22-2-220222200222-22-2-2-2-2-2-2-2200000000-22-20000002i−2i00002i−2i2i−2i002-200000000002i−2i2i−2i2i−2i2-20000000000
χ242-22-22-2-220222200222-22-2-2-2-2-2-2-2200000000-22-2000000−2i2i0000−2i2i−2i2i002-20000000000−2i2i−2i2i−2i2i2-20000000000
χ252-22-22-2-220222200222-22-2-2-2-2-2-2-2200000000-22-200002i−2i002i−2i2i−2i000000-2200002i−2i2i−2i2i−2i000000-220000000000
χ262-22-22-2-220222200222-22-2-2-2-2-2-2-2200000000-22-20000−2i2i00−2i2i−2i2i000000-220000−2i2i−2i2i−2i2i000000-220000000000
χ272-22-2-111-102-1-12−i3i32-1-1-22-2-21111-2-100−i3−i3i3i3001-11−i3−i3i3i3002i−2i3−3−33−ii−ii002-2−i3i3−i3i3003−3−332i−2i−ii−ii-110000000000
χ282-22-2-111-102-1-12−i3i32-1-1-22-2-21111-2-100−i3−i3i3i3001-11−i3−i3i3i300−2i2i−333−3i−ii−i002-2−i3i3−i3i300−333−3−2i2ii−ii−i-110000000000
χ292-22-2-111-102-1-12−i3i32-1-1-22-2-21111-2-100−i3−i3i3i3001-11−i3−i3i3i32i−2i00−ii−ii3−3−3300-22i3−i3i3−i32i−2i−ii−ii003−3−331-10000000000
χ302-22-2-111-102-1-12−i3i32-1-1-22-2-21111-2-100−i3−i3i3i3001-11−i3−i3i3i3−2i2i00i−ii−i−333−300-22i3−i3i3−i3−2i2ii−ii−i00−333−31-10000000000
χ312-22-2-111-102-1-12i3−i32-1-1-22-2-21111-2-100i3i3−i3−i3001-11i3i3−i3−i3002i−2i−333−3−ii−ii002-2i3−i3i3−i300−333−32i−2i−ii−ii-110000000000
χ322-22-2-111-102-1-12i3−i32-1-1-22-2-21111-2-100i3i3−i3−i3001-11i3i3−i3−i300−2i2i3−3−33i−ii−i002-2i3−i3i3−i3003−3−33−2i2ii−ii−i-110000000000
χ332-22-2-111-102-1-12i3−i32-1-1-22-2-21111-2-100i3i3−i3−i3001-11i3i3−i3−i32i−2i00−ii−ii−333−300-22−i3i3−i3i32i−2i−ii−ii00−333−31-10000000000
χ342-22-2-111-102-1-12i3−i32-1-1-22-2-21111-2-100i3i3−i3−i3001-11i3i3−i3−i3−2i2i00i−ii−i3−3−3300-22−i3i3−i3i3−2i2ii−ii−i003−3−331-10000000000
χ35444444444111-244111-2-2111111-2-2111111-2-2-2-2-2-2-2-2-222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ36444444444111-244111-2-2111111-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111111000000000000
χ37444444444-2-2-2144-2-2-211-2-2-2-2-2-211-2-2-2-2-2-2111111111000000000000000000000000000000000022-1-1-1-10000
χ38444444444-2-2-2144-2-2-211-2-2-2-2-2-211-2-2-2-2-2-21111111110000000000000000000000000000000000-2-211110000
χ3944444444-4111-2-4-4111-2-2111111-2-2-1-1-1-1-1-122-2-2-2222222-2-22222-2-2-2-200000000-1-1-1-1-1-1111111000000000000
χ4044444444-4111-2-4-4111-2-2111111-2-2-1-1-1-1-1-122-2-2-22222-2-222-2-2-2-2222200000000111111-1-1-1-1-1-1000000000000
χ4144444444-4-2-2-21-4-4-2-2-211-2-2-2-2-2-211222222-1-1111-1-1-1-100000000000000000000000000000000002-2-1-1110000
χ4244444444-4-2-2-21-4-4-2-2-211-2-2-2-2-2-211222222-1-1111-1-1-1-10000000000000000000000000000000000-2211-1-10000
χ434444-2-2-2-241−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1+3i32−1−3i32−1+3i32-2111−1−3i32−1+3i32−1−3i32−1+3i32-2-211111112222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i300000000-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000
χ444444-2-2-2-241−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1+3i32−1−3i32−1+3i32-2111−1−3i32−1+3i32−1−3i32−1+3i32-2-21111111-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i30000000011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ454444-2-2-2-241−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1−3i32−1+3i32−1−3i32-2111−1+3i32−1−3i32−1+3i32−1−3i32-2-211111112222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i300000000-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000
χ464444-2-2-2-241−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1−3i32−1+3i32−1−3i32-2111−1+3i32−1−3i32−1+3i32−1−3i32-2-21111111-2-2-2-21−i31−i31+i31+i31−i31−i31+i31+i30000000011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ474444-2-2-2-2-41−1−3i32−1+3i32-2221−1−3i32−1+3i32-2-211−1−3i32−1+3i32−1−3i32−1+3i32-21-1-11+3i321−3i321+3i321−3i3222111-1-1-1-122-2-2−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i300000000-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ484444-2-2-2-2-41−1−3i32−1+3i32-2221−1−3i32−1+3i32-2-211−1−3i32−1+3i32−1−3i32−1+3i32-21-1-11+3i321−3i321+3i321−3i3222111-1-1-1-1-2-2221+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i30000000011−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000
χ494444-2-2-2-2-41−1+3i32−1−3i32-2221−1+3i32−1−3i32-2-211−1+3i32−1−3i32−1+3i32−1−3i32-21-1-11−3i321+3i321−3i321+3i3222111-1-1-1-122-2-2−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i300000000-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ504444-2-2-2-2-41−1+3i32−1−3i32-2221−1+3i32−1−3i32-2-211−1+3i32−1−3i32−1+3i32−1−3i32-21-1-11−3i321+3i321−3i321+3i3222111-1-1-1-1-2-2221−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i30000000011−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000
χ5144-4-4-2-22204-2-2400-4224-44-4-2-222-4-200000000-22200000000000000004i−4i00−2i−2i2i2i000000000000000000000000
χ5244-4-4-2-22204-2-2400-4224-44-4-2-222-4-200000000-2220000000000000000−4i4i002i2i−2i−2i000000000000000000000000
χ534-44-44-4-440111-2001112-2-1-1-1-1-1-12-23-33-3-33002-2200002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000−ii−ii−ii−ii−ii−ii000000000000
χ544-44-44-4-440111-2001112-2-1-1-1-1-1-12-23-33-3-33002-220000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000i−ii−ii−ii−ii−ii−i000000000000
χ554-44-44-4-440111-2001112-2-1-1-1-1-1-12-2-33-333-3002-2200002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000−ii−ii−iii−ii−ii−i000000000000
χ564-44-44-4-440111-2001112-2-1-1-1-1-1-12-2-33-333-3002-220000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000i−ii−ii−i−ii−ii−ii000000000000
χ574-44-4-222-201−1−3i32−1+3i32-2−2i32i31−1−3i32−1+3i322-2-1-11+3i321−3i321+3i321−3i32213-3−3−i323−i323+i32−3+i3200-11-1i3i3−i3−i32i−2i2i−2i2ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400000000−ii−ζ22ζ22−ζ14ζ14−ii−ζ22ζ22−ζ14ζ14000000000000
χ584-44-4-222-201−1−3i32−1+3i32-2−2i32i31−1−3i32−1+3i322-2-1-11+3i321−3i321+3i321−3i32213-3−3−i323−i323+i32−3+i3200-11-1i3i3−i3−i3−2i2i−2i2i−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400000000i−iζ22−ζ22ζ14−ζ14i−iζ22−ζ22ζ14−ζ14000000000000
χ594-44-4-222-201−1−3i32−1+3i32-22i3−2i31−1−3i32−1+3i322-2-1-11+3i321−3i321+3i321−3i3221-333+i32−3+i32−3−i323−i3200-11-1−i3−i3i3i32i−2i−2i2i2ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ1400000000−ii−ζ22ζ22−ζ14ζ14i−iζ22−ζ22ζ14−ζ14000000000000
χ604-44-4-222-201−1−3i32−1+3i32-22i3−2i31−1−3i32−1+3i322-2-1-11+3i321−3i321+3i321−3i3221-333+i32−3+i32−3−i323−i3200-11-1−i3−i3i3i3−2i2i2i−2i−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ1400000000i−iζ22−ζ22ζ14−ζ14−ii−ζ22ζ22−ζ14ζ14000000000000
χ614-44-4-222-201−1+3i32−1−3i32-2−2i32i31−1+3i32−1−3i322-2-1-11−3i321+3i321−3i321+3i3221-333−i32−3−i32−3+i323+i3200-11-1i3i3−i3−i32i−2i−2i2i2ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ2200000000−ii−ζ14ζ14−ζ22ζ22i−iζ14−ζ14ζ22−ζ22000000000000
χ624-44-4-222-201−1+3i32−1−3i32-2−2i32i31−1+3i32−1−3i322-2-1-11−3i321+3i321−3i321+3i3221-333−i32−3−i32−3+i323+i3200-11-1i3i3−i3−i3−2i2i2i−2i−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ2200000000i−iζ14−ζ14ζ22−ζ22−ii−ζ14ζ14−ζ22ζ22000000000000
χ634-44-4-222-201−1+3i32−1−3i32-22i3−2i31−1+3i32−1−3i322-2-1-11−3i321+3i321−3i321+3i32213-3−3+i323+i323−i32−3−i3200-11-1−i3−i3i3i32i−2i2i−2i2ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200000000−ii−ζ14ζ14−ζ22ζ22−ii−ζ14ζ14−ζ22ζ22000000000000
χ644-44-4-222-201−1+3i32−1−3i32-22i3−2i31−1+3i32−1−3i322-2-1-11−3i321+3i321−3i321+3i32213-3−3+i323+i323−i32−3−i3200-11-1−i3−i3i3i3−2i2i−2i2i−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200000000i−iζ14−ζ14ζ22−ζ22i−iζ14−ζ14ζ22−ζ22000000000000
χ654-4-444-44-40444400-4-4-4-4-4-44-4-4444400000000-4-44000000000000000000000000000000000000000000000000
χ664-4-444-44-40-2-2-2100222-1-12-222-2-2110000003-3-1-113-33-3000000000000000000000000000000000000−i3i3−i3i30000
χ674-4-444-44-40-2-2-2100222-1-12-222-2-2110000003-3-1-113-33-3000000000000000000000000000000000000i3−i3i3−i30000
χ684-4-444-44-40-2-2-2100222-1-12-222-2-211000000-33-1-11-33-33000000000000000000000000000000000000−i3i3i3−i30000
χ694-4-444-44-40-2-2-2100222-1-12-222-2-211000000-33-1-11-33-33000000000000000000000000000000000000i3−i3−i3i30000
χ704-4-44-22-2204-2-2400-422-4-4-4422-2-24-20000000022-20000000000000000000023−23−2323000000000000000000000000
χ714-4-44-22-2204-2-2400-422-4-4-4422-2-24-20000000022-200000000000000000000−232323−23000000000000000000000000
χ728888-4-4-4-48-4222-4-4-42222-4-422222-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000
χ738888-4-4-4-4-8-422244-42222-4-422222-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000
χ7488-8-888-8-80222-400-2-2-2-442-222-2-24-400000000-444000000000000000000000000000000000000000000000000
χ7588-8-888-8-80-4-4-42004442-2-44-4-444-22000000002-2-2000000000000000000000000000000000000000000000000
χ7688-8-8-4-44402−1−3i3−1+3i3-400-21+3i31−3i3-442-2−1−3i3−1+3i31+3i31−3i342000000002-2-2000000000000000000000000000000000000000000000000
χ7788-8-8-4-44402−1+3i3−1−3i3-400-21−3i31+3i3-442-2−1+3i3−1−3i31−3i31+3i342000000002-2-2000000000000000000000000000000000000000000000000
χ7888-8-8-4-4440-4222004-2-22-2-4422-2-2-2-100000000-111−3i33i33i3−3i300000000000000000000000000000000000000000000
χ7988-8-8-4-4440-4222004-2-22-2-4422-2-2-2-100000000-1113i3−3i3−3i33i300000000000000000000000000000000000000000000
χ808-88-88-8-880-4-4-4200-4-4-4-22444444-2200000000-22-2000000000000000000000000000000000000000000000000
χ818-88-8-444-40-4222−4i34i3-422-2244-2-2-2-2-2-1002i32i3−2i3−2i3001-11−i3−i3i3i300000000000000000000000000000000000000000000
χ828-88-8-444-40-42224i3−4i3-422-2244-2-2-2-2-2-100−2i3−2i32i32i3001-11i3i3−i3−i300000000000000000000000000000000000000000000
χ838-8-888-88-80222-400-2-2-244-22-2-222-4-40000000044-4000000000000000000000000000000000000000000000000
χ848-8-88-44-4402−1−3i3−1+3i3-400-21+3i31−3i344-221+3i31−3i3−1−3i3−1+3i3-4200000000-2-22000000000000000000000000000000000000000000000000
χ858-8-88-44-4402−1+3i3−1−3i3-400-21−3i31+3i344-221−3i31+3i3−1+3i3−1−3i3-4200000000-2-22000000000000000000000000000000000000000000000000
χ868-8-88-44-440-4222004-2-2-2-24-4-2-2222-10000006-611-1-33-3300000000000000000000000000000000000000000000
χ878-8-88-44-440-4222004-2-2-2-24-4-2-2222-1000000-6611-13-33-300000000000000000000000000000000000000000000

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