Finite Group Databasebeta

← Group #13180909

Character table — Group #13180909

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222233444446666666121218183366666669912121212121818181818181836365454448888888121216161616162424242424242448487272448888888121216161616162424242424242448487272
order122336666443666624412121212612242226666664466666244121212126122436633666612123666661212121212126126123663366661212366666121212121212612612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-1
χ3111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1
χ4111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111
χ511-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-11
χ611-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-1
χ711-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-1
χ811-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-11
χ92222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-100
χ102222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-200001100
χ11222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000
χ12222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000
χ1322-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-1100
χ1422-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-100
χ1522-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-1110000
χ1622-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-10000
χ172-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i000000
χ182-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i000000
χ192-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−30000
χ202-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−330000
χ212-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−330000
χ222-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−30000
χ23444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000
χ2444-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-10000000000044-4-2-222-2-200121-1-100000000000
χ254-404-2002-400-20200000000000004-404-2002-400-20200000000000004-404-2002-400-20200000000000004-404-2002-400-2020000000000000
χ264-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i3000000000004-40-2-2−2i32i3220010-1i3−i300000000000
χ274-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i3000000000004-40-2-22i3−2i3220010-1−i3i300000000000
χ28111111111111111111111111111111111111111111111111111111−1+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
χ291111111111111111-11-11111-1-1-1-11111111111111111-11-11111-1-1-1-1−1+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+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+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−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ30111111111-1-1111111-11-1-1-1-111-1-1111111111-1-1111111-11-1-1-1-111-1-1−1+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+i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ31111111111-1-111111-1-1-1-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1-1-1-111−1+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−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ3211-111-1-111111-11-1-11-1-111-1-11-1-1111-111-1-111111-11-1-11-1-111-1-11-1-11−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ3311-111-1-111111-11-1-1-1-1111-1-1-111-111-111-1-111111-11-1-1-1-1111-1-1-111-1−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32
χ3411-111-1-111-1-11-11-1-111-1-1-1111-11-111-111-1-111-1-11-11-1-111-1-1-1111-11-1−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32
χ3511-111-1-111-1-11-11-1-1-111-1-111-11-1111-111-1-111-1-11-11-1-1-111-1-111-11-11−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32
χ362222-122-1200-1-1-1-1-12020000-1-1002222-122-1200-1-1-1-1-12020000-1-100−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i32−1+i3001−i321−i321−i321−i321−i32−1+i30−1+i300001−i321−i3200−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i32−1−i3001+i321+i321+i321+i321+i32−1−i30−1−i300001+i321+i3200
χ372222-122-1200-1-1-1-1-1-20-2000011002222-122-1200-1-1-1-1-1-20-200001100−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i32−1+i3001−i321−i321−i321−i321−i321−i301−i30000−1+i32−1+i3200−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i32−1−i3001+i321+i321+i321+i321+i321+i301+i30000−1−i32−1−i3200
χ38222-12-1-12-122-12-1-1-1020-1-1-1-10000222-12-1-12-122-12-1-1-1020-1-1-1-10000−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i321−i320−1+i301−i321−i321−i321−i320000−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i321+i320−1−i301+i321+i321+i321+i320000
χ39222-12-1-12-1-2-2-12-1-1-10-2011110000222-12-1-12-1-2-2-12-1-1-10-2011110000−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i31−i31−i32−1+i31−i321−i321−i3201−i30−1+i32−1+i32−1+i32−1+i320000−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i31+i31+i32−1−i31+i321+i321+i3201+i30−1−i32−1−i32−1−i32−1−i320000
χ4022-22-1-2-2-1200-11-11120-20000-110022-22-1-2-2-1200-11-11120-20000-1100−1+i3−1+i31−i3−1+i31−i321−i31−i31−i32−1+i3001−i32−1+i321−i32−1+i32−1+i32−1+i301−i300001−i32−1+i3200−1−i3−1−i31+i3−1−i31+i321+i31+i31+i32−1−i3001+i32−1−i321+i32−1−i32−1−i32−1−i301+i300001+i32−1−i3200
χ4122-22-1-2-2-1200-11-111-20200001-10022-22-1-2-2-1200-11-111-20200001-100−1+i3−1+i31−i3−1+i31−i321−i31−i31−i32−1+i3001−i32−1+i321−i32−1+i32−1+i321−i30−1+i30000−1+i321−i3200−1−i3−1−i31+i3−1−i31+i321+i31+i31+i32−1−i3001+i32−1−i321+i32−1−i32−1−i321+i30−1−i30000−1−i321+i3200
χ4222-2-12112-122-1-2-1110-20-1-111000022-2-12112-122-1-2-1110-20-1-1110000−1+i3−1+i31−i31−i32−1+i3−1+i32−1+i32−1+i31−i32−1+i3−1+i31−i321−i31−i32−1+i32−1+i3201−i301−i321−i32−1+i32−1+i320000−1−i3−1−i31+i31+i32−1−i3−1−i32−1−i32−1−i31+i32−1−i3−1−i31+i321+i31+i32−1−i32−1−i3201+i301+i321+i32−1−i32−1−i320000
χ4322-2-12112-1-2-2-1-2-11102011-1-1000022-2-12112-1-2-2-1-2-11102011-1-10000−1+i3−1+i31−i31−i32−1+i3−1+i32−1+i32−1+i31−i321−i31−i31−i321−i31−i32−1+i32−1+i320−1+i30−1+i32−1+i321−i321−i320000−1−i3−1−i31+i31+i32−1−i3−1−i32−1−i32−1−i31+i321+i31+i31+i321+i31+i32−1−i32−1−i320−1−i30−1−i32−1−i321+i321+i320000
χ442-202200-2-22i−2i20-2000002i−2i0000002-202200-2-22i−2i20-2000002i−2i000000−1+i31−i30−1+i3−1+i3001−i31−i32ζ7−2ζ7−1+i301−i3000002ζ7−2ζ7000000−1−i31+i30−1−i3−1−i3001+i31+i32ζ11−2ζ11−1−i301+i3000002ζ11−2ζ11000000
χ452-202200-2-2−2i2i20-200000−2i2i0000002-202200-2-2−2i2i20-200000−2i2i000000−1+i31−i30−1+i3−1+i3001−i31−i3−2ζ72ζ7−1+i301−i300000−2ζ72ζ7000000−1−i31+i30−1−i3−1−i3001+i31+i3−2ζ112ζ11−1−i301+i300000−2ζ112ζ11000000
χ462-20-12−i3i3-212i−2i-101−i3i3000−ii3−300002-20-12−i3i3-212i−2i-101−i3i3000−ii3−30000−1+i31−i301−i32−1+i33+i32−3−i321−i3−1+i322ζ7−2ζ71−i320−1+i323+i32−3−i32000−ζ7ζ7−ζ7−2ζ11ζ7+2ζ110000−1−i31+i301+i32−1−i3−3+i323−i321+i3−1−i322ζ11−2ζ111+i320−1−i32−3+i323−i32000−ζ11ζ112ζ7+ζ11−2ζ7−ζ110000
χ472-20-12−i3i3-21−2i2i-101−i3i3000i−i−3300002-20-12−i3i3-21−2i2i-101−i3i3000i−i−330000−1+i31−i301−i32−1+i33+i32−3−i321−i3−1+i32−2ζ72ζ71−i320−1+i323+i32−3−i32000ζ7−ζ7ζ7+2ζ11−ζ7−2ζ110000−1−i31+i301+i32−1−i3−3+i323−i321+i3−1−i32−2ζ112ζ111+i320−1−i32−3+i323−i32000ζ11−ζ11−2ζ7−ζ112ζ7+ζ110000
χ482-20-12i3−i3-212i−2i-101i3−i3000−ii−3300002-20-12i3−i3-212i−2i-101i3−i3000−ii−330000−1+i31−i301−i32−1+i3−3−i323+i321−i3−1+i322ζ7−2ζ71−i320−1+i32−3−i323+i32000−ζ7ζ7ζ7+2ζ11−ζ7−2ζ110000−1−i31+i301+i32−1−i33−i32−3+i321+i3−1−i322ζ11−2ζ111+i320−1−i323−i32−3+i32000−ζ11ζ11−2ζ7−ζ112ζ7+ζ110000
χ492-20-12i3−i3-21−2i2i-101i3−i3000i−i3−300002-20-12i3−i3-21−2i2i-101i3−i3000i−i3−30000−1+i31−i301−i32−1+i3−3−i323+i321−i3−1+i32−2ζ72ζ71−i320−1+i32−3−i323+i32000ζ7−ζ7−ζ7−2ζ11ζ7+2ζ110000−1−i31+i301+i32−1−i33−i32−3+i321+i3−1−i32−2ζ112ζ111+i320−1−i323−i32−3+i32000ζ11−ζ112ζ7+ζ11−2ζ7−ζ110000
χ50444-2-2-2-2-2-2001-211100000000000444-2-2-2-2-2-2001-211100000000000−2+2i3−2+2i3−2+2i31−i31−i31−i31−i31−i31−i300−1+i321−i3−1+i32−1+i32−1+i3200000000000−2−2i3−2−2i3−2−2i31+i31+i31+i31+i31+i31+i300−1−i321+i3−1−i32−1−i32−1−i3200000000000
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χ1051212-12-6-666-6-600363-3-300000000000-4-4422-2-22200-1-2-11100000000000000000000000000000000000000000000000000000000000000000
χ10612-12012-6006-1200-6060000000000000-440-4200-240020-20000000000000000000000000000000000000000000000000000000000000000000
χ10712-120-6-6−6i36i3660030-33i3−3i300000000000-440222i3−2i3-2-200-101−i3i300000000000000000000000000000000000000000000000000000000000000000
χ10812-120-6-66i3−6i3660030-3−3i33i300000000000-44022−2i32i3-2-200-101i3−i300000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.