Finite Group Databasebeta

← Group #13169347

Character table — Group #13169347

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212124444121212121212121212121212121212124412121212121212121212121212121212121212122444412121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111-11-1-1-1-1-111111111-11-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1111111111-1-1-1-11-1-1-11-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-1-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-11111111-1-11111-1-1-1-111-1-1-1-1-1-1-11111111-1-1-1-11111-1-111-111-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-111-1-111111111-1-1-11-1-11111-1-111-1-1-1-1-111-1-111-1-1-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-111111111-11-1-111-1-111-1-111-1-11-11-1-111-1-1-1-11-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-111-11111111-1-11-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-11-1-1-1-1-11111-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1-11-1-111-1-11111-1-111-11-1-1-1-1-111111-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-111-11111111-1-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-111-1-111-1-11111111-111-1-111-1-111-1-1111-11-1-111-1-1-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-111-1-111-1-1111111111-111-1-1-1-111-1-111-1-1-111-1-111-1-1-111-1
χ17222222-12-1-1222-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1202222-1-1-1-10000222200000000-1-102-1-1-1-1-1-1-1-100002000200-1-100-1000
χ18222222-12-1-1222-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-120-2-2-2-211-1-10000222200000000-110-21111-1-1-1-10000-2000-20011001000
χ19222222-12-1-1222-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-202222-1-1110000-2-2-2-2000000001-102-1-1-1-111110000-2000-20011001000
χ20222222-12-1-1222-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2-2-211110000-2-2-2-200000000110-21111111100002000200-1-100-1000
χ21222222-12-1-1222-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-202-2-2-2-1-1-1-1000022-2-200000000110211-1-1-1-1110000-2000200-1-1001000
χ22222222-12-1-1222-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-20-222211-1-1000022-2-2000000001-10-2-1-111-1-11100002000-2001100-1000
χ23222222-12-1-1222-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111202-2-2-2-1-1110000-2-22200000000-110211-1-111-1-100002000-2001100-1000
χ24222222-12-1-1222-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-2111120-222211110000-2-22200000000-1-10-2-1-11111-1-10000-2000200-1-1001000
χ2522222-12222-12-12-12-12-12-1-12-1-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-12200000022-1-1-1-1-1-1-1-12222-1-1-1-120200000-1-1-1-1-1-1-1-1020000000-1-10000
χ2622222-12222-12-12-12-12-12-1-12-1-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-12-2000000221111-1-1-1-1-2-2-2-2111120-200000-1-1-1-111110-20000000110000
χ2722222-12222-12-12-12-12-12-1-12-1-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-22000000-2-2-1-1-1-1111122-2-21111-202000001111-1-1-1-10-20000000110000
χ2822222-12222-12-12-12-12-12-1-12-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2-2000000-2-211111111-2-222-1-1-1-1-20-20000011111111020000000-1-10000
χ2922222-12222-12-12-12-12-1-2-1-12-1-122-1-1112222-1-1-1-1-2-211-2-2111111-2-200000022-1-111-1-1112222-1-1-1-1-20-200000-1-111-1-1110-20000000110000
χ3022222-12222-12-12-12-12-1-2-1-12-1-122-1-11122-2-2-1-1-1-1-2-211-2-2111111-220000002211-1-1-1-111-2-2-2-21111-20200000-1-11111-1-1020000000-1-10000
χ3122222-12222-12-12-12-12-1-2-1-12-1-122-1-111-2-222-1-1-1-1-2-211-2-21111112-2000000-2-2-1-11111-1-122-2-2111120-20000011-1-1-1-111020000000-1-10000
χ3222222-12222-12-12-12-12-1-2-1-12-1-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111122000000-2-211-1-111-1-1-2-222-1-1-1-12020000011-1-111-1-10-20000000110000
χ332222-122-1222-1222-1-1-122-1-1-122-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10222-1-1220022220000-1-100000002-1-1-1-1-1-10000-1-1-1-100220-1-100000-100
χ342222-122-1222-1222-1-1-122-1-1-122-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-102-2-211-2-20022220000-1-10000000-2-1111110000-1-1-1-100-2-201100000100
χ352222-122-1222-1222-1-1-122-1-1-122-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-222-1-12200-2-2-2-2000011000000021-1-1-1-1-10000111100-2-201100000100
χ362222-122-1222-1222-1-1-122-1-1-122-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-211-2-200-2-2-2-20000110000000-21111110000111100220-1-100000-100
χ372222-122-1222-1222-1-1-12-2-1-1-122-1-12-1-2-20022-1-1-1-1-21-2-2111111110-22-211220022-2-20000-1-10000000-21-111-1-10000-1-11100-2201100000-100
χ382222-122-1222-1222-1-1-12-2-1-1-122-1-12-1-2-20022-1-1-1-1-21-2-2111111110-2-22-1-1-2-20022-2-20000-1-10000000211-1-1110000-1-111002-20-1-100000100
χ392222-122-1222-1222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111022-2112200-2-2220000110000000-2-1-111-1-1000011-1-1002-20-1-100000100
χ402222-122-1222-1222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-1-1-1-1-21-2-21111111102-22-1-1-2-200-2-22200001100000002-11-1-111000011-1-100-2201100000-100
χ412-22-2222-22-22-2-2-2-222220-2-2-2-22-22-22002i−2i2-22-2-22000000000000000000002i−2i2-2002i−2i002-22i−2i2i2i−2i−2i000000002i−2i002-200000000000000000
χ422-22-2222-22-22-2-2-2-222220-2-2-2-22-22-22002i−2i-222-2-22000000000000000000002i−2i-22002i−2i00-22−2i2i−2i−2i2i2i000000002i−2i00-2200000000000000000
χ432-22-2222-22-22-2-2-2-222220-2-2-2-22-22-2200−2i2i2-22-2-2200000000000000000000−2i2i2-200−2i2i002-2−2i2i−2i−2i2i2i00000000−2i2i002-200000000000000000
χ442-22-2222-22-22-2-2-2-222220-2-2-2-22-22-2200−2i2i-222-2-2200000000000000000000−2i2i-2200−2i2i00-222i−2i2i2i−2i−2i00000000−2i2i00-2200000000000000000
χ452-22-22-12-22-2-1-21-212-12-1011-21-1-221-1−i3i32i−2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000002i−2i-11−i3i3−ii3−32-22i−2i−i−iii00000000−ii3−3-11−i3i30000000003−30000
χ462-22-22-12-22-2-1-21-212-12-1011-21-1-221-1−i3i32i−2i-22-111-100−i3i300−i3i3−i3−i3i3i3000000002i−2i1-1i3−i3−ii3−3-22−2i2iii−i−i00000000−ii3−31-1i3−i3000000000−330000
χ472-22-22-12-22-2-1-21-212-12-1011-21-1-221-1−i3i3−2i2i2-2-111-100−i3i300−i3i3−i3−i3i3i300000000−2i2i-11−i3i3i−i−332-2−2i2iii−i−i00000000i−i−33-11−i3i3000000000−330000
χ482-22-22-12-22-2-1-21-212-12-1011-21-1-221-1−i3i3−2i2i-22-111-100−i3i300−i3i3−i3−i3i3i300000000−2i2i1-1i3−i3i−i−33-222i−2i−i−iii00000000i−i−331-1i3−i30000000003−30000
χ492-22-22-12-22-2-1-21-212-12-1011-21-1-221-1i3−i32i−2i2-2-111-100i3−i300i3−i3i3i3−i3−i3000000002i−2i-11i3−i3−ii−332-22i−2i−i−iii00000000−ii−33-11i3−i3000000000−330000
χ502-22-22-12-22-2-1-21-212-12-1011-21-1-221-1i3−i32i−2i-22-111-100i3−i300i3−i3i3i3−i3−i3000000002i−2i1-1−i3i3−ii−33-22−2i2iii−i−i00000000−ii−331-1−i3i30000000003−30000
χ512-22-22-12-22-2-1-21-212-12-1011-21-1-221-1i3−i3−2i2i2-2-111-100i3−i300i3−i3i3i3−i3−i300000000−2i2i-11i3−i3i−i3−32-2−2i2iii−i−i00000000i−i3−3-11i3−i30000000003−30000
χ522-22-22-12-22-2-1-21-212-12-1011-21-1-221-1i3−i3−2i2i-22-111-100i3−i300i3−i3i3i3−i3−i300000000−2i2i1-1−i3i3i−i3−3-222i−2i−i−iii00000000i−i3−31-1−i3i3000000000−330000
χ5344444-2-24-2-2-24-2-2-24-2-214-2-2-211-2-21-2-2-244001111-2411-2-2-2-2111140000000-2-20000-2-2-2-200000000-2000000011110000000000000000000
χ5444444-2-24-2-2-24-2-2-24-2-214-2-2-211-2-21-2-2-2-4-4001111-2411-2-2-2-21111-4000000022000022220000000020000000-1-1-1-10000000000000000000
χ5544444-2-24-2-2-24-2-2-24-2-21-4-2-2-211-2-21-222440011112-4-1-12222-1-1-1-1-40000000-2-20000-2-222000000002000000011-1-10000000000000000000
χ5644444-2-24-2-2-24-2-2-24-2-21-4-2-2-211-2-21-222-4-40011112-4-1-12222-1-1-1-14000000022000022-2-200000000-20000000-1-1110000000000000000000
χ574444-24-2-2-2-24-24-24-2-21-24-2-21-2-211-2-24400001111-2-2-2-211-2-211110044-2-2-2-20000000000000000000-20-2111100000000000000000000000
χ584444-24-2-2-2-24-24-24-2-21-24-2-21-2-211-2-24400001111-2-2-2-211-2-2111100-4-422220000000000000000000202-1-1-1-100000000000000000000000
χ594444-24-2-2-2-24-24-24-2-21-2-4-2-21-2-211-2-2-4-4000011112222-1-122-1-1-1-1004-422-2-2000000000000000000020-2-1-11100000000000000000000000
χ604444-24-2-2-2-24-24-24-2-21-2-4-2-21-2-211-2-2-4-4000011112222-1-122-1-1-1-100-44-2-2220000000000000000000-20211-1-100000000000000000000000
χ614444-2-24-244-2-2-24-2-21-2-2411-2-2-2-2-2-21-2-2004411114-2-2-2-2-21111110400000000-2-2-2-20000-2-200000000-20000000001111000000000000000
χ624444-2-24-244-2-2-24-2-21-2-2411-2-2-2-2-2-21-2-200-4-411114-2-2-2-2-21111110-4000000002222000022000000002000000000-1-1-1-1000000000000000
χ634444-2-24-244-2-2-24-2-21-2-2-411-2-2-2-2-2-212200441111-422222-1-1-1-1-1-10-400000000-2-2220000-2-200000000200000000011-1-1000000000000000
χ644444-2-24-244-2-2-24-2-21-2-2-411-2-2-2-2-2-212200-4-41111-422222-1-1-1-1-1-1040000000022-2-200002200000000-2000000000-1-111000000000000000
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χ784-44-4-24424-442-4-4-4-2-2-240222-442-2-4-200004-4-222-200000000000000000000004-4000000-22000000000000000000-2200000000000000000
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χ814-44-4-2-2424-4-222-42-21-2-20-1-122-22-221−2i32i300-441-1-1100−2i32i300i3−i3i3i3−i3−i300000000002-22i3−2i300002-2000000000000000000-11−i3i3000000000000000
χ824-44-4-2-2424-4-222-42-21-2-20-1-122-22-2212i3−2i3004-41-1-11002i3−2i300−i3i3−i3−i3i3i30000000000-222i3−2i30000-220000000000000000001-1−i3i3000000000000000
χ834-44-4-2-2424-4-222-42-21-2-20-1-122-22-2212i3−2i300-441-1-11002i3−2i300−i3i3−i3−i3i3i300000000002-2−2i32i300002-2000000000000000000-11i3−i3000000000000000
χ844-4-444444-4-4-4-444-4-44440-44-44-44-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
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χ904-4-44-244-2-4-4-4244-42-2-2402-224-4-22-42000000-22-2200000000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000000000
χ914-4-44-24-2-222-424-2-42-21-202-2-1-221-1220000001-11-100003i−3i003i−3i3i−3i0000−2i32i323−230000000000000000000000i3−i3−3300000000000000000000000
χ924-4-44-24-2-222-424-2-42-21-202-2-1-221-1220000001-11-100003i−3i003i−3i3i−3i00002i3−2i3−23230000000000000000000000−i3i33−300000000000000000000000
χ934-4-44-24-2-222-424-2-42-21-202-2-1-221-1220000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i3−23230000000000000000000000i3−i33−300000000000000000000000
χ944-4-44-24-2-222-424-2-42-21-202-2-1-221-1220000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i323−230000000000000000000000−i3i3−3300000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4-84-44844-4-8-4-420-44-4-2-2442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-444-4-8-4-8484-42-40-44244-2-2-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-484-884-44-8-442-4-402-2-44444-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-444-44-444-4422202-22-2-2-2-22-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-444-44-444-4422202-22-2-2-2-22-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-44-4484-84-8-4-42-4044-24-4-224-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-44-44444-42220-2-2-2-22-22-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-44-44444-42220-2-2-2-22-22-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-48444-8-4-44-8-4-4204-442-2-44-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-4-8-844-48442-4-40-224-44-444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-44444-4-4442220-22-22-22-2-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-44444-4-4442220-22-22-22-2-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000

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