Finite Group Databasebeta

← Group #13147217

Character table — Group #13147217

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222226666666666121212121212121212121212121212121212121212121212121818181824242424242424242424242424242424242424247272727272727272108108
order12223446661212121234466612121212334666666121212121212121212121212121212122222336666661212121212121212121212126666666644
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111111111111111−1−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+i3211
χ4111111111111111111111111−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111111111-1-1-1-1−1−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−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1
χ5111111111111111111111111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111111111111111−1+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−i3211
χ6111111111111111111111111−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111111111-1-1-1-1−1+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+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1
χ711111-1-1111-1-1-1-1111111-1-1-1-111-111111111-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1
χ811111-1-1111-1-1-1-1111111-1-1-1-111-111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11
χ911111-1-1111-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1
χ1011111-1-1111-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11
χ1111111-1-1111-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1
χ1211111-1-1111-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11
χ1322222222222222-122-1-1-1-1-1-1-12222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ1422222222222222-122-1-1-1-1-1-1-1−1−i3−1+i32−1−i3−1−i3−1+i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i320000000000
χ1522222222222222-122-1-1-1-1-1-1-1−1+i3−1−i32−1+i3−1+i3−1−i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i320000000000
χ1622222-2-2222-2-2-2-2-122-1-1-1111122-222222222-2-2-1-1-1-1-1-11111110000-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ1722222-2-2222-2-2-2-2-122-1-1-11111−1−i3−1+i3-2−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322-2-2-1-1-1-1-1-111111100001+i321−i321+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000000
χ1822222-2-2222-2-2-2-2-122-1-1-11111−1+i3−1−i3-2−1+i3−1+i3−1−i3−1−i3−1+i3−1−i322-2-2-1-1-1-1-1-111111100001−i321+i321−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000000000
χ1922-2-222-22-2-222-2-22002-2-222-2-2-1-101111-1-100000000000000002-22-2-1-11111-1-11-11-111-1-111-1-11-11-11-11-100
χ2022-2-222-22-2-222-2-22002-2-222-2-2-1-101111-1-10000000000000000-22-22-1-11111-1-11-11-111-1-111-1-1-11-11-11-1100
χ2122-2-222-22-2-222-2-22002-2-222-2-21+i321−i320−1−i32−1−i32−1+i32−1+i321+i321−i3200000000000000002-22-21+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i3200
χ2222-2-222-22-2-222-2-22002-2-222-2-21+i321−i320−1−i32−1−i32−1+i32−1+i321+i321−i320000000000000000-22-221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i3200
χ2322-2-222-22-2-222-2-22002-2-222-2-21−i321+i320−1+i32−1+i32−1−i32−1−i321−i321+i3200000000000000002-22-21−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i3200
χ2422-2-222-22-2-222-2-22002-2-222-2-21−i321+i320−1+i32−1+i32−1−i32−1−i321−i321+i320000000000000000-22-221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i3200
χ2522-2-22-222-2-2-2-2222002-2-2-2-222-1-101111-1-100000000000000002-2-22-1-11111-1-1-11-11-1-111-1-1111-1-111-1-1100
χ2622-2-22-222-2-2-2-2222002-2-2-2-222-1-101111-1-10000000000000000-222-2-1-11111-1-1-11-11-1-111-1-111-111-1-111-100
χ2722-2-22-222-2-2-2-2222002-2-2-2-2221+i321−i320−1−i32−1−i32−1+i32−1+i321+i321−i3200000000000000002-2-221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i3200
χ2822-2-22-222-2-2-2-2222002-2-2-2-2221+i321−i320−1−i32−1−i32−1+i32−1+i321+i321−i320000000000000000-222-21+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i3200
χ2922-2-22-222-2-2-2-2222002-2-2-2-2221−i321+i320−1+i32−1+i32−1−i32−1−i321−i321+i3200000000000000002-2-221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i3200
χ3022-2-22-222-2-2-2-2222002-2-2-2-2221−i321+i320−1+i32−1+i32−1−i32−1−i321−i321+i320000000000000000-222-21−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i3200
χ312-2-22200-22-2000022-2-22-200002202-22-2-2-22-200222-2-2-20000000000222-22-2-2-20000000000000000000000
χ322-2-22200-22-2000022-2-22-20000−1−i3−1+i30−1−i31+i3−1+i31−i31+i31−i32-200222-2-2-20000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000000000000000
χ332-2-22200-22-2000022-2-22-20000−1+i3−1−i30−1+i31−i3−1−i31+i31−i31+i32-200222-2-2-20000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000000000000000
χ342-2-22200-22-20000-12-21-113−33−32202-22-2-2-22-200-1-1-1111333−3−3−30000-1-1-11-111100003−33−33−33−30000000000
χ352-2-22200-22-20000-12-21-113−33−3−1−i3−1+i30−1−i31+i3−1+i31−i31+i31−i32-200-1-1-1111333−3−3−300001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i3200002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ110000000000
χ362-2-22200-22-20000-12-21-113−33−3−1+i3−1−i30−1+i31−i3−1−i31+i31−i31+i32-200-1-1-1111333−3−3−300001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i320000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ110000000000
χ372-2-22200-22-20000-12-21-11−33−332202-22-2-2-22-200-1-1-1111−3−3−33330000-1-1-11-11110000−33−33−33−330000000000
χ382-2-22200-22-20000-12-21-11−33−33−1−i3−1+i30−1−i31+i3−1+i31−i31+i31−i32-200-1-1-1111−3−3−333300001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i320000−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ110000000000
χ392-2-22200-22-20000-12-21-11−33−33−1+i3−1−i30−1+i31−i3−1−i31+i31−i31+i32-200-1-1-1111−3−3−333300001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i320000ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ110000000000
χ40333333333333333-1-1333333300-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000000000000000-1-1
χ41333333333333333-1-1333333300-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3000000000000000000000000000011
χ4233333-3-3333-3-3-3-33-1-1333-3-3-3-3001000000-1-111-1-1-1-1-1-111111133-3-30000000000000000000000000000-11
χ4333333-3-3333-3-3-3-33-1-1333-3-3-3-3001000000-1-111-1-1-1-1-1-1111111-3-33300000000000000000000000000001-1
χ4444-4-444-44-4-444-4-4-200-222-2-222-2-202222-2-20000000000000000000011-1-1-1-1112-22-2-1-111-1-1110000000000
χ4544-4-444-44-4-444-4-4-200-222-2-2221+i31−i30−1−i3−1−i3−1+i3−1+i31+i31−i300000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i31+i3−1+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i320000000000
χ4644-4-444-44-4-444-4-4-200-222-2-2221−i31+i30−1+i3−1+i3−1−i3−1−i31−i31+i300000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i31−i3−1−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i320000000000
χ4744-4-44-444-4-4-4-444-200-22222-2-2-2-202222-2-20000000000000000000011-1-1-1-111-22-2211-1-111-1-10000000000
χ4844-4-44-444-4-4-4-444-200-22222-2-21+i31−i30−1−i3−1−i3−1+i3−1+i31+i31−i300000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i3−1−i31−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i320000000000
χ4944-4-44-444-4-4-4-444-200-22222-2-21−i31+i30−1+i3−1+i3−1−i3−1−i31−i31+i300000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i3−1+i31+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i320000000000
χ504-44-4400-4-440000400-4-440000-2-202-22-22200000000000000000000-2-22-22-2220000000000000000000000
χ514-44-4400-4-440000400-4-4400001+i31−i30−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000000000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i30000000000000000000000
χ524-44-4400-4-440000400-4-4400001−i31+i30−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000000000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i30000000000000000000000
χ534-44-4400-4-440000-20022-223−23−2323-2-202-22-2220000000000000000000011-11-11-1-100003−3−333−3−330000000000
χ544-44-4400-4-440000-20022-223−23−23231+i31−i30−1−i31+i3−1+i31−i3−1−i3−1+i300000000000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i3200002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ110000000000
χ554-44-4400-4-440000-20022-223−23−23231−i31+i30−1+i31−i3−1−i31+i3−1+i3−1−i300000000000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i320000−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ110000000000
χ564-44-4400-4-440000-20022-2−232323−23-2-202-22-2220000000000000000000011-11-11-1-10000−333−3−333−30000000000
χ574-44-4400-4-440000-20022-2−232323−231+i31−i30−1−i31+i3−1+i31−i3−1−i3−1+i300000000000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i320000−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ110000000000
χ584-44-4400-4-440000-20022-2−232323−231−i31+i30−1+i31−i3−1−i31+i3−1+i3−1−i300000000000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i320000ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ110000000000
χ5966666666666666-3-2-2-3-3-3-3-3-3-300-2000000-2-2-2-21111111111110000000000000000000000000000000000
χ6066666-6-6666-6-6-6-6-3-2-2-3-3-33333002000000-2-222111111-1-1-1-1-1-10000000000000000000000000000000000
χ616666-366-3-3-3-3-3-3-30660000000006000000-3-3-3-30000000000000000000000000000000000000000000000
χ626666-366-3-3-3-3-3-3-30-2-2000000000-200000011114-2-24-2-24-2-24-2-20000000000000000000000000000000000
χ636666-366-3-3-3-3-3-3-30-2-2000000000-20000001111-24-2-24-2-24-2-24-20000000000000000000000000000000000
χ646666-366-3-3-3-3-3-3-30-2-2000000000-20000001111-2-24-2-24-2-24-2-240000000000000000000000000000000000
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χ726-6-66-3003-3333−3333−3306-60000000000000000-3333−330000000000000000000000000000000000000000000000
χ736-6-66-3003-3333−3333−330-2200000000000000001-1−334-2-2-422023−230−23230000000000000000000000000000000000
χ746-6-66-3003-3333−3333−330-2200000000000000001-1−33-24-22-42−23023230−230000000000000000000000000000000000
χ756-6-66-3003-3333−3333−330-2200000000000000001-1−33-2-2422-423−230−232300000000000000000000000000000000000
χ766-6-66-3003-33−3333−333306-60000000000000000-33−33330000000000000000000000000000000000000000000000
χ776-6-66-3003-33−3333−33330-2200000000000000001-13−34-2-2-4220−2323023−230000000000000000000000000000000000
χ786-6-66-3003-33−3333−33330-2200000000000000001-13−3-24-22-42230−23−230230000000000000000000000000000000000
χ796-6-66-3003-33−3333−33330-2200000000000000001-13−3-2-2422-4−2323023−2300000000000000000000000000000000000
χ801212-12-12-612-12-666-6-666000000000000000000000000000000000000000000000000000000000000000000000
χ811212-12-12-6-1212-66666-6-6000000000000000000000000000000000000000000000000000000000000000000000
χ8212-1212-12-60066-663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-60066-6−636363−63000000000000000000000000000000000000000000000000000000000000000000000

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