Finite Group Databasebeta

← Group #13181121

Character table — Group #13181121

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112224444444444488888881212121212121818181824242424242436363636363636108108112224444444444488888881212121212121818181824242424242436363636363636108108
order122363333666666636666662466121244121266612121244121212121288222666666666666666666662466121244121266612121244121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111111111111111111111111-1-11-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1
χ411111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111
χ511-1111111-1-1-111111-1-1-11-1-11-111-1-1-11-1-1111-1-1-11-1111-1-11-111-1111111-1-1-111111-1-1-11-1-11-111-1-1-11-1-1111-1-1-11-1111-1-11-1
χ611-1111111-1-1-111111-1-1-11-1-11-111-1-1-11-1-1111-1-1-1-111-1-111-1111-1111111-1-1-111111-1-1-11-1-11-111-1-1-11-1-1111-1-1-1-111-1-111-11
χ711-1111111-1-1-111111-1-1-11-1-1-11-1-111-11-1-1-1-1-11111-1111-1-1-1111-1111111-1-1-111111-1-1-11-1-1-11-1-111-11-1-1-1-1-11111-1111-1-1-11
χ811-1111111-1-1-111111-1-1-11-1-1-11-1-111-11-1-1-1-1-1111-111-1-1111-111-1111111-1-1-111111-1-1-11-1-1-11-1-111-11-1-1-1-1-1111-111-1-1111-1
χ922222222222222222222222000000-2-2-2-200000000-200000022222222222222222222222000000-2-2-2-200000000-2000000
χ10222-1-122-1-1-1222-1-12-12-1-1-1-1-100−i3i3−i3i3-2-2110−i3i30−i3i3001000000222-1-122-1-1-1222-1-12-12-1-1-1-1-100−i3i3−i3i3-2-2110−i3i30−i3i3001000000
χ11222-1-122-1-1-1222-1-12-12-1-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3001000000222-1-122-1-1-1222-1-12-12-1-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3001000000
χ12222-1-122-1-1-1222-1-12-12-1-1-1-1-122-1-1-1-122-1-12-1-12-1-100-1000000222-1-122-1-1-1222-1-12-12-1-1-1-1-122-1-1-1-122-1-12-1-12-1-100-1000000
χ13222-1-122-1-1-1222-1-12-12-1-1-1-1-1-2-2111122-1-1-211-21100-1000000222-1-122-1-1-1222-1-12-12-1-1-1-1-1-2-2111122-1-1-211-21100-1000000
χ1422-2222222-2-2-222222-2-2-22-2-20000002-22200000000-200000022-2222222-2-2-222222-2-2-22-2-20000002-22200000000-2000000
χ1522-2-1-122-1-11-2-22-1-12-1-211-11100−i3i3i3−i32-2-1-10−i3i30i3−i300100000022-2-1-122-1-11-2-22-1-12-1-211-11100−i3i3i3−i32-2-1-10−i3i30i3−i3001000000
χ1622-2-1-122-1-11-2-22-1-12-1-211-11100i3−i3−i3i32-2-1-10i3−i30−i3i300100000022-2-1-122-1-11-2-22-1-12-1-211-11100i3−i3−i3i32-2-1-10i3−i30−i3i3001000000
χ1722-2-1-122-1-11-2-22-1-12-1-211-1112-2-1-111-22112-1-1-21100-100000022-2-1-122-1-11-2-22-1-12-1-211-1112-2-1-111-22112-1-1-21100-1000000
χ1822-2-1-122-1-11-2-22-1-12-1-211-111-2211-1-1-2211-2112-1-100-100000022-2-1-122-1-11-2-22-1-12-1-211-111-2211-1-1-2211-2112-1-100-1000000
χ19444441-2-2-2411-2-2-211-2-2-21110000000000000000220-1-1-1-100444441-2-2-2411-2-2-211-2-2-21110000000000000000220-1-1-1-100
χ20444441-2-2-2411-2-2-211-2-2-21110000000000000000-2-20111100444441-2-2-2411-2-2-211-2-2-21110000000000000000-2-20111100
χ2144444-21114-2-2111-2-2111-2-2-22222220000-1-1-1-1-1-100000000044444-21114-2-2111-2-2111-2-2-22222220000-1-1-1-1-1-1000000000
χ2244444-21114-2-2111-2-2111-2-2-2-2-2-2-2-2-2000011111100000000044444-21114-2-2111-2-2111-2-2-2-2-2-2-2-2-20000111111000000000
χ23444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i3211122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i3211122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000
χ24444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32111-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32111-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000
χ25444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i3211122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i3211122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000
χ26444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32111-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32111-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000
χ2744-4441-2-2-2-4-1-1-2-2-2112221-1-100000000000000002-20-1-1110044-4441-2-2-2-4-1-1-2-2-2112221-1-100000000000000002-20-1-11100
χ2844-4441-2-2-2-4-1-1-2-2-2112221-1-10000000000000000-22011-1-10044-4441-2-2-2-4-1-1-2-2-2112221-1-10000000000000000-22011-1-100
χ2944-444-2111-422111-2-2-1-1-1-2222-222-2-20000-1-1-111100000000044-444-2111-422111-2-2-1-1-1-2222-222-2-20000-1-1-1111000000000
χ3044-444-2111-422111-2-2-1-1-1-222-22-2-2220000111-1-1-100000000044-444-2111-422111-2-2-1-1-1-222-22-2-2220000111-1-1-1000000000
χ3144-4-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-21-11+3i321−3i321-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i3200000000044-4-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-21-11+3i321−3i321-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000
χ3244-4-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-21-11+3i321−3i321-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i3200000000044-4-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-21-11+3i321−3i321-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000
χ3344-4-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-21-11−3i321+3i321-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i3200000000044-4-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-21-11−3i321+3i321-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000
χ3444-4-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-21-11−3i321+3i321-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i3200000000044-4-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-21-11−3i321+3i321-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000
χ354-404-41-2-2-203-3222-11000-13-300000000000000000003−33−3004-404-41-2-2-203-3222-11000-13-300000000000000000003−33−300
χ364-404-41-2-2-203-3222-11000-13-30000000000000000000−33−33004-404-41-2-2-203-3222-11000-13-30000000000000000000−33−3300
χ374-404-41-2-2-20-33222-11000-1-3300000000000000000003−3−33004-404-41-2-2-20-33222-11000-1-3300000000000000000003−3−3300
χ384-404-41-2-2-20-33222-11000-1-330000000000000000000−333−3004-404-41-2-2-20-33222-11000-1-330000000000000000000−333−300
χ394-404-44444000-4-4-4-44000-40000000000000000000000000004-404-44444000-4-4-4-44000-4000000000000000000000000000
χ404-40-2244-2-2000-422-4-20002000000000023−230000000000000004-40-2244-2-2000-422-4-20002000000000023−23000000000000000
χ414-40-2244-2-2000-422-4-200020000000000−23230000000000000004-40-2244-2-2000-422-4-200020000000000−2323000000000000000
χ42888-4-42-422-422-4222-1-422-1-1-10000000000000000000000000888-4-42-422-422-4222-1-422-1-1-10000000000000000000000000
χ4388-8-4-42-4224-2-2-4222-14-2-2-111000000000000000000000000088-8-4-42-4224-2-2-4222-14-2-2-1110000000000000000000000000
χ448-808-8-4222000-2-2-24-400040000000000000000000000000008-808-8-4222000-2-2-24-40004000000000000000000000000000
χ458-80-442-42206-64-2-2-2-10001-3300000000000000000000000008-80-442-42206-64-2-2-2-10001-330000000000000000000000000
χ468-80-442-4220-664-2-2-2-100013-300000000000000000000000008-80-442-4220-664-2-2-2-100013-30000000000000000000000000
χ478-80-44-42−1−3i3−1+3i3000-21+3i31−3i342000-20000000000000000000000000008-80-44-42−1−3i3−1+3i3000-21+3i31−3i342000-2000000000000000000000000000
χ488-80-44-42−1+3i3−1−3i3000-21−3i31+3i342000-20000000000000000000000000008-80-44-42−1+3i3−1−3i3000-21−3i31+3i342000-2000000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ50111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ5111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-111
χ5211111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-11111-1-1
χ5311-1111111-1-1-111111-1-1-11-1-11-111-1-1-11-1-1111-1-1-11-1111-1-11-1-1-11-1-1-1-1-1-1111-1-1-1-1-1111-111-11-1-1111-111-1-1-1111-11-1-1-111-11
χ5411-1111111-1-1-111111-1-1-11-1-11-111-1-1-11-1-1111-1-1-1-111-1-111-11-1-11-1-1-1-1-1-1111-1-1-1-1-1111-111-11-1-1111-111-1-1-11111-1-111-1-11-1
χ5511-1111111-1-1-111111-1-1-11-1-1-11-1-111-11-1-1-1-1-11111-1111-1-1-11-1-11-1-1-1-1-1-1111-1-1-1-1-1111-1111-111-1-11-111111-1-1-1-11-1-1-1111-1
χ5611-1111111-1-1-111111-1-1-11-1-1-11-1-111-11-1-1-1-1-1111-111-1-1111-1-1-11-1-1-1-1-1-1111-1-1-1-1-1111-1111-111-1-11-111111-1-1-11-1-111-1-1-11
χ5722222222222222222222222000000-2-2-2-200000000-2000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000002222000000002000000
χ58222-1-122-1-1-1222-1-12-12-1-1-1-1-100−i3i3−i3i3-2-2110−i3i30−i3i3001000000-2-2-211-2-2111-2-2-211-21-21111100i3−i3i3−i322-1-10i3−i30i3−i300-1000000
χ59222-1-122-1-1-1222-1-12-12-1-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3001000000-2-2-211-2-2111-2-2-211-21-21111100−i3i3−i3i322-1-10−i3i30−i3i300-1000000
χ60222-1-122-1-1-1222-1-12-12-1-1-1-1-122-1-1-1-122-1-12-1-12-1-100-1000000-2-2-211-2-2111-2-2-211-21-211111-2-21111-2-211-211-211001000000
χ61222-1-122-1-1-1222-1-12-12-1-1-1-1-1-2-2111122-1-1-211-21100-1000000-2-2-211-2-2111-2-2-211-21-21111122-1-1-1-1-2-2112-1-12-1-1001000000
χ6222-2222222-2-2-222222-2-2-22-2-20000002-22200000000-2000000-2-22-2-2-2-2-2-2222-2-2-2-2-2222-222000000-22-2-2000000002000000
χ6322-2-1-122-1-11-2-22-1-12-1-211-11100−i3i3i3−i32-2-1-10−i3i30i3−i3001000000-2-2211-2-211-122-211-212-1-11-1-100i3−i3−i3i3-22110i3−i30−i3i300-1000000
χ6422-2-1-122-1-11-2-22-1-12-1-211-11100i3−i3−i3i32-2-1-10i3−i30−i3i3001000000-2-2211-2-211-122-211-212-1-11-1-100−i3i3i3−i3-22110−i3i30i3−i300-1000000
χ6522-2-1-122-1-11-2-22-1-12-1-211-1112-2-1-111-22112-1-1-21100-1000000-2-2211-2-211-122-211-212-1-11-1-1-2211-1-12-2-1-1-2112-1-1001000000
χ6622-2-1-122-1-11-2-22-1-12-1-211-111-2211-1-1-2211-2112-1-100-1000000-2-2211-2-211-122-211-212-1-11-1-12-2-1-1112-2-1-12-1-1-211001000000
χ67444441-2-2-2411-2-2-211-2-2-21110000000000000000220-1-1-1-100-4-4-4-4-4-1222-4-1-1222-1-1222-1-1-10000000000000000-2-20111100
χ68444441-2-2-2411-2-2-211-2-2-21110000000000000000-2-20111100-4-4-4-4-4-1222-4-1-1222-1-1222-1-1-10000000000000000220-1-1-1-100
χ6944444-21114-2-2111-2-2111-2-2-22222220000-1-1-1-1-1-1000000000-4-4-4-4-42-1-1-1-422-1-1-122-1-1-1222-2-2-2-2-2-20000111111000000000
χ7044444-21114-2-2111-2-2111-2-2-2-2-2-2-2-2-20000111111000000000-4-4-4-4-42-1-1-1-422-1-1-122-1-1-12222222220000-1-1-1-1-1-1000000000
χ71444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i3211122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000-4-4-4222-11+3i321−3i32222-11+3i321−3i322-1-11+3i321−3i32-1-1-1-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000
χ72444-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32111-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000-4-4-4222-11+3i321−3i32222-11+3i321−3i322-1-11+3i321−3i32-1-1-122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000
χ73444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i3211122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000-4-4-4222-11−3i321+3i32222-11−3i321+3i322-1-11−3i321+3i32-1-1-1-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000
χ74444-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32111-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000-4-4-4222-11−3i321+3i32222-11−3i321+3i322-1-11−3i321+3i32-1-1-122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000
χ7544-4441-2-2-2-4-1-1-2-2-2112221-1-100000000000000002-20-1-11100-4-44-4-4-1222411222-1-1-2-2-2-1110000000000000000-22011-1-100
χ7644-4441-2-2-2-4-1-1-2-2-2112221-1-10000000000000000-22011-1-100-4-44-4-4-1222411222-1-1-2-2-2-11100000000000000002-20-1-11100
χ7744-444-2111-422111-2-2-1-1-1-2222-222-2-20000-1-1-1111000000000-4-44-4-42-1-1-14-2-2-1-1-1221112-2-2-22-2-2220000111-1-1-1000000000
χ7844-444-2111-422111-2-2-1-1-1-222-22-2-2220000111-1-1-1000000000-4-44-4-42-1-1-14-2-2-1-1-1221112-2-22-222-2-20000-1-1-1111000000000
χ7944-4-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-21-11+3i321−3i321-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000-4-44222-11+3i321−3i32-2-2-2-11+3i321−3i322-11−1−3i32−1+3i32-111-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000
χ8044-4-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-21-11+3i321−3i321-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000-4-44222-11+3i321−3i32-2-2-2-11+3i321−3i322-11−1−3i32−1+3i32-1112-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000
χ8144-4-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-21-11−3i321+3i321-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000-4-44222-11−3i321+3i32-2-2-2-11−3i321+3i322-11−1+3i32−1−3i32-111-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000
χ8244-4-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-21-11−3i321+3i321-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000-4-44222-11−3i321+3i32-2-2-2-11−3i321+3i322-11−1+3i32−1−3i32-1112-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000
χ834-404-41-2-2-203-3222-11000-13-300000000000000000003−33−300-440-44-12220-33-2-2-21-10001-330000000000000000000−33−3300
χ844-404-41-2-2-203-3222-11000-13-30000000000000000000−33−3300-440-44-12220-33-2-2-21-10001-3300000000000000000003−33−300
χ854-404-41-2-2-20-33222-11000-1-3300000000000000000003−3−3300-440-44-122203-3-2-2-21-100013-30000000000000000000−333−300
χ864-404-41-2-2-20-33222-11000-1-330000000000000000000−333−300-440-44-122203-3-2-2-21-100013-300000000000000000003−3−3300
χ874-404-44444000-4-4-4-44000-4000000000000000000000000000-440-44-4-4-4-40004444-40004000000000000000000000000000
χ884-40-2244-2-2000-422-4-20002000000000023−23000000000000000-4402-2-4-4220004-2-242000-20000000000−2323000000000000000
χ894-40-2244-2-2000-422-4-200020000000000−2323000000000000000-4402-2-4-4220004-2-242000-2000000000023−23000000000000000
χ90888-4-42-422-422-4222-1-422-1-1-10000000000000000000000000-8-8-844-24-2-24-2-24-2-2-214-2-21110000000000000000000000000
χ9188-8-4-42-4224-2-2-4222-14-2-2-1110000000000000000000000000-8-8844-24-2-2-4224-2-2-21-4221-1-10000000000000000000000000
χ928-808-8-4222000-2-2-24-40004000000000000000000000000000-880-884-2-2-2000222-44000-4000000000000000000000000000
χ938-80-442-42206-64-2-2-2-10001-330000000000000000000000000-8804-4-24-2-20-66-42221000-13-30000000000000000000000000
χ948-80-442-4220-664-2-2-2-100013-30000000000000000000000000-8804-4-24-2-206-6-42221000-1-330000000000000000000000000
χ958-80-44-42−1−3i3−1+3i3000-21+3i31−3i342000-2000000000000000000000000000-8804-44-21+3i31−3i30002−1−3i3−1+3i3-4-20002000000000000000000000000000
χ968-80-44-42−1+3i3−1−3i3000-21−3i31+3i342000-2000000000000000000000000000-8804-44-21−3i31+3i30002−1+3i3−1−3i3-4-20002000000000000000000000000000

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