Finite Group Databasebeta

← Group #13180832

Character table — Group #13180832

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222222233334444466666666666688888888888899121212121216161616161616161616161618181818182424242424242424242424243636363672727272108108108108
order12233666622443666624666666121212123336666666664466666333666666666412121212121212121212121212121212244461212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111-1-1111111-1111111-1-1-1-1111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111-1-1111111-1111111-1-1-1-1111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-111-1-11111111-11-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111111-111-1-1111111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-11-11-11-1-111-1
χ611-111-1-11111111-11-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111111-111-1-1111111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-11-11-111-1-11
χ711-111-1-11111-1-11-11-1-1-1111-1-111-1-111111-1-1-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-1-11111111-11-11-11-11-1-11
χ811-111-1-11111-1-11-11-1-1-1111-1-111-1-111111-1-1-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1111111-11-11-11-11-111-1
χ9222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1022222222222-2-2222222-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2111111111111000000000000
χ112222-122-122200-1-1-1-1-1202222-1-1000022222222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000002222-1-1-1-10000
χ122222-122-122200-1-1-1-1-1202222-1-1000022222222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-2-2-2-211110000
χ13222-12-1-12-12222-12-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-12-1-1222-1-1-1-12-1-12-1-122-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1000000000000
χ14222-12-1-12-12222-12-1-1-122-1-1-1-122-1-1-1-1-12-1-1-122-1-1-12-1222-1-1-1-1-12-1-12-1-1-122-1-12-1-1-1-1-1-122-1-1-1-122-1-1000000000000
χ15222-12-1-12-12222-12-1-1-122-1-1-1-122-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-12-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122000000000000
χ16222-12-1-12-122-2-2-12-1-1-12-2-1-1-1-12211112-1-122-1-1-1-12-1-1-2-22-1-1-1-12-1-12-1-122-1-1-1-1-21111-2-21111-2-21111000000000000
χ17222-12-1-12-122-2-2-12-1-1-12-2-1-1-1-1221111-12-1-1-122-1-1-12-1-2-22-1-1-1-1-12-1-12-1-1-122-1-1-2111111-2-21111-2-211000000000000
χ18222-12-1-12-122-2-2-12-1-1-12-2-1-1-1-1221111-1-12-1-1-1-122-1-12-2-22-1-1-1-1-1-12-1-12-1-1-1-122-211111111-2-21111-2-2000000000000
χ1922-222-2-22222222-22-2-2-2-222-2-22222-2-2-1-1-1111111-1-1-122-222-2-2-1-1-1-1-1-1111111-222-2-2-1-1-1-1-1-1111111000000000000
χ2022-222-2-22222-2-22-22-2-2-2222-2-222-2-222-1-1-1111111-1-1-1-2-2-222-2-2-1-1-1-1-1-11111112-2-222111111-1-1-1-1-1-1000000000000
χ2122-22-1-2-2-122200-11-111-2022-2-2-1-10000222-2-2-2-2-2-2222001-1-111-1-1-1-1-1-1111111000000000000000002-22-2-11-110000
χ2222-22-1-2-2-122200-11-111-2022-2-2-1-10000222-2-2-2-2-2-2222001-1-111-1-1-1-1-1-111111100000000000000000-22-221-11-10000
χ2322-2-12112-12222-1-2-111-2-2-1-11122-1-1112-1-1-2-211112-1-122-2-1-1112-1-12-1-1-2-21111-2-1-11122-1-1-1-1-2-21111000000000000
χ2422-2-12112-12222-1-2-111-2-2-1-11122-1-111-12-111-2-211-12-122-2-1-111-12-1-12-111-2-211-2-1-111-1-122-1-111-2-211000000000000
χ2522-2-12112-12222-1-2-111-2-2-1-11122-1-111-1-121111-2-2-1-1222-2-1-111-1-12-1-121111-2-2-2-1-111-1-1-1-1221111-2-2000000000000
χ2622-2-12112-122-2-2-1-2-111-22-1-1112211-1-12-1-1-2-211112-1-1-2-2-2-1-1112-1-12-1-1-2-21111211-1-1-2-2111122-1-1-1-1000000000000
χ2722-2-12112-122-2-2-1-2-111-22-1-1112211-1-1-12-111-2-211-12-1-2-2-2-1-111-12-1-12-111-2-211211-1-111-2-211-1-122-1-1000000000000
χ2822-2-12112-122-2-2-1-2-111-22-1-1112211-1-1-1-121111-2-2-1-12-2-2-2-1-111-1-12-1-121111-2-2211-1-11111-2-2-1-1-1-122000000000000
χ292-202200-2-22-22i−2i20-200002-2002-22i−2i00222000000-2-2-22i−2i02-200222-2-2-200000002i−2i002i−2i2i−2i2i−2i000000000000000000
χ302-202200-2-22-22i−2i20-200002-2002-22i−2i00-1-1-1−i3i3−i3i3−i3i31112i−2i02-200-1-1-1111−i3i3−i3i3−i3i302i−2i00−ii−ii−ii3−33−33−3000000000000
χ312-202200-2-22-22i−2i20-200002-2002-22i−2i00-1-1-1i3−i3i3−i3i3−i31112i−2i02-200-1-1-1111i3−i3i3−i3i3−i302i−2i00−ii−ii−ii−33−33−33000000000000
χ322-202200-2-22-2−2i2i20-200002-2002-2−2i2i00222000000-2-2-2−2i2i02-200222-2-2-20000000−2i2i00−2i2i−2i2i−2i2i000000000000000000
χ332-202200-2-22-2−2i2i20-200002-2002-2−2i2i00-1-1-1−i3i3−i3i3−i3i3111−2i2i02-200-1-1-1111−i3i3−i3i3−i3i30−2i2i00i−ii−ii−i−33−33−33000000000000
χ342-202200-2-22-2−2i2i20-200002-2002-2−2i2i00-1-1-1i3−i3i3−i3i3−i3111−2i2i02-200-1-1-1111i3−i3i3−i3i3−i30−2i2i00i−ii−ii−i3−33−33−3000000000000
χ352-20-12−i3i3-212-22i−2i-101−i3i300-11−i3i32-2−ii3−32-1-100−i3i3i3−i3-2112i−2i0-11−i3i32-1-1-21100−i3i3i3−i30−ii3−32i−2i−ii−ii003−3−33000000000000
χ362-20-12−i3i3-212-22i−2i-101−i3i300-11−i3i32-2−ii3−3-12-1i3−i300−i3i31-212i−2i0-11−i3i3-12-11-21i3−i300−i3i30−ii3−3−ii2i−2i−ii−33003−3000000000000
χ372-20-12−i3i3-212-22i−2i-101−i3i300-11−i3i32-2−ii3−3-1-12−i3i3i3−i30011-22i−2i0-11−i3i3-1-1211-2−i3i3i3−i3000−ii3−3−ii−ii2i−2i3−3−3300000000000000
χ382-20-12−i3i3-212-2−2i2i-101−i3i300-11−i3i32-2i−i−332-1-100−i3i3i3−i3-211−2i2i0-11−i3i32-1-1-21100−i3i3i3−i30i−i−33−2i2ii−ii−i00−333−3000000000000
χ392-20-12−i3i3-212-2−2i2i-101−i3i300-11−i3i32-2i−i−33-12-1i3−i300−i3i31-21−2i2i0-11−i3i3-12-11-21i3−i300−i3i30i−i−33i−i−2i2ii−i3−300−33000000000000
χ402-20-12−i3i3-212-2−2i2i-101−i3i300-11−i3i32-2i−i−33-1-12−i3i3i3−i30011-2−2i2i0-11−i3i3-1-1211-2−i3i3i3−i3000i−i−33i−ii−i−2i2i−333−300000000000000
χ412-20-12i3−i3-212-22i−2i-101i3−i300-11i3−i32-2−ii−332-1-100i3−i3−i3i3-2112i−2i0-11i3−i32-1-1-21100i3−i3−i3i30−ii−332i−2i−ii−ii00−333−3000000000000
χ422-20-12i3−i3-212-22i−2i-101i3−i300-11i3−i32-2−ii−33-12-1−i3i300i3−i31-212i−2i0-11i3−i3-12-11-21−i3i300i3−i30−ii−33−ii2i−2i−ii3−300−33000000000000
χ432-20-12i3−i3-212-22i−2i-101i3−i300-11i3−i32-2−ii−33-1-12i3−i3−i3i30011-22i−2i0-11i3−i3-1-1211-2i3−i3−i3i3000−ii−33−ii−ii2i−2i−333−300000000000000
χ442-20-12i3−i3-212-2−2i2i-101i3−i300-11i3−i32-2i−i3−32-1-100i3−i3−i3i3-211−2i2i0-11i3−i32-1-1-21100i3−i3−i3i30i−i3−3−2i2ii−ii−i003−3−33000000000000
χ452-20-12i3−i3-212-2−2i2i-101i3−i300-11i3−i32-2i−i3−3-12-1−i3i300i3−i31-21−2i2i0-11i3−i3-12-11-21−i3i300i3−i30i−i3−3i−i−2i2ii−i−33003−3000000000000
χ462-20-12i3−i3-212-2−2i2i-101i3−i300-11i3−i32-2i−i3−3-1-12i3−i3−i3i30011-2−2i2i0-11i3−i3-1-1211-2i3−i3−i3i3000i−i3−3i−ii−i−2i2i3−3−3300000000000000
χ47333333333-1-13333333-13-1-1-1-1-1-13333000000000000-1-1-1-1-1-1-1000000000000-1-1-1-1-100000000000011-1-111-1-111-1-1
χ48333333333-1-13333333-13-1-1-1-1-1-13333000000000000-1-1-1-1-1-1-1000000000000-1-1-1-1-1000000000000-1-111-1-111-1-111
χ49333333333-1-1-3-333333-1-3-1-1-1-1-1-1-3-3-3-300000000000011-1-1-1-1-10000000000001111100000000000011-1-111-1-1-1-111
χ50333333333-1-1-3-333333-1-3-1-1-1-1-1-1-3-3-3-300000000000011-1-1-1-1-100000000000011111000000000000-1-111-1-11111-1-1
χ5133-333-3-333-1-1333-33-3-31-3-1-111-1-133-3-3000000000000-1-11-1-1110000000000001-1-1110000000000001-1-111-1-11-11-11
χ5233-333-3-333-1-1333-33-3-31-3-1-111-1-133-3-3000000000000-1-11-1-1110000000000001-1-111000000000000-111-1-111-11-11-1
χ5333-333-3-333-1-1-3-33-33-3-313-1-111-1-1-3-333000000000000111-1-111000000000000-111-1-10000000000001-1-111-1-111-11-1
χ5433-333-3-333-1-1-3-33-33-3-313-1-111-1-1-3-333000000000000111-1-111000000000000-111-1-1000000000000-111-1-111-1-11-11
χ554444-244-244400-2-2-2-2-2404444-2-20000-2-2-2-2-2-2-2-2-2-2-2-200-2-2-2-2-211111111111100000000000000000000000000000
χ56444-2-2-2-2-2-244001-211140-2-2-2-2-2-200004-2-244-2-2-2-24-2-200-21111-211-211-2-2111100000000000000000000000000000
χ57444-2-2-2-2-2-244001-211140-2-2-2-2-2-20000-24-2-2-244-2-2-24-200-211111-211-2111-2-21100000000000000000000000000000
χ58444-2-2-2-2-2-244001-211140-2-2-2-2-2-20000-2-24-2-2-2-244-2-2400-2111111-211-21111-2-200000000000000000000000000000
χ5944-44-2-4-4-244400-22-222-4044-4-4-2-20000-2-2-2222222-2-2-2002-2-222111111-1-1-1-1-1-100000000000000000000000000000
χ6044-4-2-222-2-24400121-1-1-40-2-222-2-200004-2-2-4-422224-2-200211-1-1-211-21122-1-1-1-100000000000000000000000000000
χ6144-4-2-222-2-24400121-1-1-40-2-222-2-20000-24-222-4-422-24-200211-1-11-211-21-1-122-1-100000000000000000000000000000
χ6244-4-2-222-2-24400121-1-1-40-2-222-2-20000-2-242222-4-4-2-2400211-1-111-211-2-1-1-1-12200000000000000000000000000000
χ634-404-2002-44-400-20200004-400-220000444000000-4-4-4000-2200-2-2-222200000000000000000000000000000000000
χ644-404-2002-44-400-20200004-400-220000-2-2-2−2i32i3−2i32i3−2i32i3222000-2200111-1-1-1i3−i3i3−i3i3−i300000000000000000000000000000
χ654-404-2002-44-400-20200004-400-220000-2-2-22i3−2i32i3−2i32i3−2i3222000-2200111-1-1-1−i3i3−i3i3−i3i300000000000000000000000000000
χ664-40-2-2−2i32i3224-40010-1i3−i300-22−2i32i3-2200004-2-200−2i32i32i3−2i3-4220001-1i3−i3-2112-1-100i3−i3−i3i300000000000000000000000000000
χ674-40-2-2−2i32i3224-40010-1i3−i300-22−2i32i3-220000-24-22i3−2i300−2i32i32-420001-1i3−i31-21-12-1−i3i300i3−i300000000000000000000000000000
χ684-40-2-2−2i32i3224-40010-1i3−i300-22−2i32i3-220000-2-24−2i32i32i3−2i30022-40001-1i3−i311-2-1-12i3−i3−i3i30000000000000000000000000000000
χ694-40-2-22i3−2i3224-40010-1−i3i300-222i3−2i3-2200004-2-2002i3−2i3−2i32i3-4220001-1−i3i3-2112-1-100−i3i3i3−i300000000000000000000000000000
χ704-40-2-22i3−2i3224-40010-1−i3i300-222i3−2i3-220000-24-2−2i32i3002i3−2i32-420001-1−i3i31-21-12-1i3−i300−i3i300000000000000000000000000000
χ714-40-2-22i3−2i3224-40010-1−i3i300-222i3−2i3-220000-2-242i3−2i3−2i32i30022-40001-1−i3i311-2-1-12−i3i3i3−i30000000000000000000000000000000
χ726666-366-36-2-200-3-3-3-3-3-20-2-2-2-211000000000000000000111110000000000000000000000000000022-2-2-1-1110000
χ736666-366-36-2-200-3-3-3-3-3-20-2-2-2-2110000000000000000001111100000000000000000000000000000-2-22211-1-10000
χ74666-36-3-36-3-2-266-36-3-3-3-261111-2-2-3-3-3-3000000000000-2-2-21111000000000000-21111000000000000000000000000
χ75666-36-3-36-3-2-2-6-6-36-3-3-3-2-61111-2-2333300000000000022-211110000000000002-1-1-1-1000000000000000000000000
χ7666-66-3-6-6-36-2-200-33-33320-2-22211000000000000000000-111-1-1000000000000000000000000000002-2-22-111-10000
χ7766-66-3-6-6-36-2-200-33-33320-2-22211000000000000000000-111-1-100000000000000000000000000000-222-21-1-110000
χ7866-6-36336-3-2-266-3-6-3332-611-1-1-2-2-3-333000000000000-2-2211-1-1000000000000211-1-1000000000000000000000000
χ7966-6-36336-3-2-2-6-6-3-6-3332611-1-1-2-233-3-300000000000022211-1-1000000000000-2-1-111000000000000000000000000
χ806-606600-6-6-226i−6i60-60000-2200-226i−6i00000000000000−2i2i0-22000000000000000−2i2i00000000000000000000000000
χ816-606600-6-6-22−6i6i60-60000-2200-22−6i6i000000000000002i−2i0-220000000000000002i−2i00000000000000000000000000
χ826-60-36−3i33i3-63-226i−6i-303−3i33i3001-1i3−i3-22−3i3i33−33000000000000−2i2i01-1i3−i30000000000000i−i−33000000000000000000000000
χ836-60-36−3i33i3-63-22−6i6i-303−3i33i3001-1i3−i3-223i−3i−33330000000000002i−2i01-1i3−i30000000000000−ii3−3000000000000000000000000
χ846-60-363i3−3i3-63-226i−6i-3033i3−3i3001-1−i3i3-22−3i3i−3333000000000000−2i2i01-1−i3i30000000000000i−i3−3000000000000000000000000
χ856-60-363i3−3i3-63-22−6i6i-3033i3−3i3001-1−i3i3-223i−3i33−330000000000002i−2i01-1−i3i30000000000000−ii−33000000000000000000000000
χ86121212-6-6-6-6-6-6-4-4003-6333-402222220000000000000000002-1-1-1-100000000000000000000000000000000000000000
χ871212-12-6-666-6-6-4-400363-3-34022-2-222000000000000000000-2-1-11100000000000000000000000000000000000000000
χ8812-12012-6006-12-4400-6060000-44002-200000000000000000002-20000000000000000000000000000000000000000000
χ8912-120-6-6−6i36i366-440030-33i3−3i3002-22i3−2i32-20000000000000000000-11−i3i300000000000000000000000000000000000000000
χ9012-120-6-66i3−6i366-440030-3−3i33i3002-2−2i32i32-20000000000000000000-11i3−i300000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).