Finite Group Databasebeta

← Group #13168378

Character table — Group #13168378

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212122444661212121212121212121212121212441212121266612121212121212121212121212244446612121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-1111111-1-1111111111111-1-1-11-11-1-111111111-1-1-11-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-11111111-1-111-1-1-1-111-1-1-1-1-1-1111-11111-1-1-1-11111-11-1-11-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-11-1-111-1-1-1-11-111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1111111-1-1-1-11-11-1-111-1-1-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11-1-11-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-111-1-111111111111-1-1-1-1-111-1-111-1-1-111-1-1-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111111111-1-1-1-11-11111-1-111-1-11-1-1-1111-1-1-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-11-1111111-1-11-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1111-1-111-1-111-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-111-1-1111-1-111-1-1111-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11-1111111-1-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-111-1-11111111111-11-1-1-1-111-1-1111-1-1-1111-1-1-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-111-1-1111111-1-1-111111-1-111-1-111-111-1-1-1-1-1-1111-11-1
χ17222222-12-122-1-12222-1-1222-1-1-1-1-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-12022220000-1-1-1-1222200000000-1-1-1-120-1-1-1-1-1-1000020200-1-10000-1000
χ18222222-12-122-1-12222-1-1222-1-1-1-1-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-1-202-2-2-20000-1-111222200000000111-1-2011-1-1-1-10000-20-2001100001000
χ19222222-12-122-1-12222-1-1222-1-1-1-1-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-120-2222000011-1-1-2-2-2-200000000-1-1-1120-1-111110000-20-2001100001000
χ20222222-12-122-1-12222-1-1222-1-1-1-1-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2-2-200001111-2-2-2-2000000001111-20111111000020200-1-10000-1000
χ21222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-20022-1-1-1-11-21111-2-2111120-2-2220000-1-11122-2-200000000-1-1-11-2011-1-1110000-20200110000-1000
χ22222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-20022-1-1-1-11-21111-2-21111-20-22-2-20000-1-1-1-122-2-200000000111120-1-1-1-111000020-200-1-100001000
χ23222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-200-2-2-1-1-1-11-21111-2-21111202-22200001111-2-22200000000-1-1-1-1-201111-1-1000020-200-1-100001000
χ24222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-200-2-2-1-1-1-11-21111-2-21111-2022-2-2000011-1-1-2-22200000000111-120-1-111-1-10000-20200110000-1000
χ2522222-12-122222-12-1-12-12-1-12-12-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12202-1-1222200220000-1-10000002-1-10-1-1-1-10000-1-1-1-1020020000-1-10-100
χ2622222-12-122222-12-1-12-12-1-12-12-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-1-220-211222200-2-20000-1-1000000-21101-1110000-1-1-1-10-200-20000110100
χ2722222-12-122222-12-1-12-12-1-12-12-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-12-202-1-1-2-2-2-200220000110000002-1-10-11-1-1000011110-200-20000110100
χ2822222-12-122222-12-1-12-12-1-12-12-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-211-2-2-2-200-2-2000011000000-2110111100001111020020000-1-10-100
χ2922222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-22200-1-1-1-1-21-2-2111111112-20-2-1-122-2-200-2-20000-1-10000002-1-1011110000-1-1110200-20000-1-10100
χ3022222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-22200-1-1-1-1-21-2-211111111-2-2021122-2-200220000-1-1000000-2110-11-1-10000-1-1110-20020000110-100
χ3122222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-2-2-200-1-1-1-1-21-2-211111111220-2-1-1-2-22200-2-20000110000002-1-101-111000011-1-10-20020000110-100
χ3222222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-2-2-200-1-1-1-1-21-2-211111111-220211-2-2220022000011000000-2110-1-1-1-1000011-1-10200-20000-1-10100
χ332222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1022000-1-1-1-12200-1-1-1-12222-1-1-1-100020200-1-1-1-1-1-1-1-10002000-1-1000000
χ342222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-102-2000-1-1-1-1-2-200111122-2-21111000-202001111-1-1-1-1000-200011000000
χ352222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-10-2200011112200-1-1-1-1-2-2-2-2111100020-200-1-1-1-11111000-200011000000
χ362222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-10-2-20001111-2-2001111-2-222-1-1-1-1000-20-200111111110002000-1-1000000
χ372222-12222-1-1222-12-1-12-2-1-1-12-122-1-1112222-1-1-1-1-2-211-2-21111110-2-2000-1-1112200-1-1112222-1-1-1-1000-20-200-1-111-1-111000-200011000000
χ382222-12222-1-1222-12-1-12-2-1-1-12-122-1-11122-2-2-1-1-1-1-2-211-2-21111110-22000-1-111-2-20011-1-122-2-2111100020-20011-1-1-1-1110002000-1-1000000
χ392222-12222-1-1222-12-1-12-2-1-1-12-122-1-111-2-222-1-1-1-1-2-211-2-211111102-200011-1-12200-1-111-2-2-2-21111000-20200-1-11111-1-10002000-1-1000000
χ402222-12222-1-1222-12-1-12-2-1-1-12-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111102200011-1-1-2-20011-1-1-2-222-1-1-1-10002020011-1-111-1-1000-200011000000
χ4122-2-2222-222-2-2-2-2-222220-2-2-2-222-2-22002-22i−2i2-2-220000000000000000002-2002i−2i002i−2i002-22i−2i2i2i−2i−2i000000002i−2i002-200000000000000000
χ4222-2-2222-222-2-2-2-2-222220-2-2-2-222-2-22002-2−2i2i2-2-220000000000000000002-200−2i2i00−2i2i002-2−2i2i−2i−2i2i2i00000000−2i2i002-200000000000000000
χ4322-2-2222-222-2-2-2-2-222220-2-2-2-222-2-2200-222i−2i2-2-22000000000000000000-22002i−2i002i−2i00-22−2i2i−2i−2i2i2i000000002i−2i00-2200000000000000000
χ4422-2-2222-222-2-2-2-2-222220-2-2-2-222-2-2200-22−2i2i2-2-22000000000000000000-2200−2i2i00−2i2i00-222i−2i2i2i−2i−2i00000000−2i2i00-2200000000000000000
χ4522-2-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i32-22i−2i-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32i−2i00−ii3−32-22i−2i−i−iii00000000−ii3−3-11−i3i300000003−3000000
χ4622-2-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i32-2−2i2i-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i3−2i2i00i−i−332-2−2i2iii−i−i00000000i−i−33-11−i3i30000000−33000000
χ4722-2-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i3-222i−2i-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i32i−2i00−ii3−3-22−2i2iii−i−i00000000−ii3−31-1i3−i30000000−33000000
χ4822-2-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i3-22−2i2i-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3−2i2i00i−i−33-222i−2i−i−iii00000000i−i−331-1i3−i300000003−3000000
χ4922-2-2-122-22-11-2-2-212-1-120111-2-12-21-1i3−i32-22i−2i-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32i−2i00−ii−332-22i−2i−i−iii00000000−ii−33-11i3−i30000000−33000000
χ5022-2-2-122-22-11-2-2-212-1-120111-2-12-21-1i3−i32-2−2i2i-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i3−2i2i00i−i3−32-2−2i2iii−i−i00000000i−i3−3-11i3−i300000003−3000000
χ5122-2-2-122-22-11-2-2-212-1-120111-2-12-21-1i3−i3-222i−2i-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i32i−2i00−ii−33-22−2i2iii−i−i00000000−ii−331-1−i3i300000003−3000000
χ5222-2-2-122-22-11-2-2-212-1-120111-2-12-21-1i3−i3-22−2i2i-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3−2i2i00i−i3−3-222i−2i−i−iii00000000i−i3−31-1−i3i30000000−33000000
χ5344444-2-2-2-244-2-2-24-2-2-214-2-2-21-211-2-24400001111-2-2-2-211-2-211114004-2-2000000-2-2000000000000-2110-201100000000000000000000000
χ5444444-2-2-2-244-2-2-24-2-2-214-2-2-21-211-2-24400001111-2-2-2-211-2-21111-400-422000000220000000000002-1-1020-1-100000000000000000000000
χ5544444-2-2-2-244-2-2-24-2-2-21-4-2-2-21-211-2-2-4-4000011112222-1-122-1-1-1-1400-4-2-200000022000000000000-211020-1-100000000000000000000000
χ5644444-2-2-2-244-2-2-24-2-2-21-4-2-2-21-211-2-2-4-4000011112222-1-122-1-1-1-1-400422000000-2-20000000000002-1-10-201100000000000000000000000
χ574444-24-24-2-2-2-2-24-24-21-24-2-21-21-2-21-2-2-200441111-2411-2-2-2-211110040000000-2-200-2-2-2-200000000000-2000011110000000000000000000
χ584444-24-24-2-2-2-2-24-24-21-24-2-21-21-2-21-2-2-200-4-41111-2411-2-2-2-2111100-40000000220022220000000000020000-1-1-1-10000000000000000000
χ594444-24-24-2-2-2-2-24-24-21-2-4-2-21-21-2-21-222004411112-4-1-12222-1-1-1-100-40000000-2-200-2-222000000000002000011-1-10000000000000000000
χ604444-24-24-2-2-2-2-24-24-21-2-4-2-21-21-2-21-22200-4-411112-4-1-12222-1-1-1-10040000000220022-2-200000000000-20000-1-1110000000000000000000
χ614444-2-24-24-2-244-2-2-21-2-2411-2-2-2-2-2-21-2-2440011114-2-2-2-2-2111111040000-2-2-2-200000000-2-200000000000-20000001111000000000000000
χ624444-2-24-24-2-244-2-2-21-2-2411-2-2-2-2-2-21-2-2-4-40011114-2-2-2-2-21111110-4000022220000000022000000000002000000-1-1-1-1000000000000000
χ634444-2-24-24-2-244-2-2-21-2-2-411-2-2-2-2-2-212244001111-422222-1-1-1-1-1-10-40000-2-22200000000-2-200000000000200000011-1-1000000000000000
χ644444-2-24-24-2-244-2-2-21-2-2-411-2-2-2-2-2-2122-4-4001111-422222-1-1-1-1-1-104000022-2-2000000002200000000000-2000000-1-111000000000000000
χ6544-4-444-2-4-24-422-4-444-2-20-4-422-2-222400004i−4i-222-20000000000000000000000−2i2i004i−4i000000000000000000−2i2i000000000000000000000
χ6644-4-444-2-4-24-422-4-444-2-20-4-422-2-22240000−4i4i-222-200000000000000000000002i−2i00−4i4i0000000000000000002i−2i000000000000000000000
χ6744-4-44-24244-4-4-42-4-2-24-2022-424-22-4-2004-400-222-20000000000000000004-40000000000-22000000000000000000-2200000000000000000
χ6844-4-44-24244-4-4-42-4-2-24-2022-424-22-4-200-4400-222-2000000000000000000-4400000000002-20000000000000000002-200000000000000000
χ6944-4-4-24-2-4-2-2222-424-21-2022-121-22-1-2−2i32i3004i−4i1-1-1100i3−i300−2i32i3i3i3−i3−i30000000000−2i2i00−2i2i23−230000000000000000i−i−330000000000000000000
χ7044-4-4-24-2-4-2-2222-424-21-2022-121-22-1-2−2i32i300−4i4i1-1-1100i3−i300−2i32i3i3i3−i3−i300000000002i−2i002i−2i−23230000000000000000−ii3−30000000000000000000
χ7144-4-4-24-2-4-2-2222-424-21-2022-121-22-1-22i3−2i3004i−4i1-1-1100−i3i3002i3−2i3−i3−i3i3i30000000000−2i2i00−2i2i−23230000000000000000i−i3−30000000000000000000
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χ7344-4-4-2-2424-22-4-422-21-2-20-1-122-2-2221−2i32i34-4001-1-1100−2i32i300i3−i3i3i3−i3−i3000000-22−2i32i300000000-220000000000000000001-1i3−i3000000000000000
χ7444-4-4-2-2424-22-4-422-21-2-20-1-122-2-2221−2i32i3-44001-1-1100−2i32i300i3−i3i3i3−i3−i30000002-22i3−2i3000000002-2000000000000000000-11−i3i3000000000000000
χ7544-4-4-2-2424-22-4-422-21-2-20-1-122-2-22212i3−2i34-4001-1-11002i3−2i300−i3i3−i3−i3i3i3000000-222i3−2i300000000-220000000000000000001-1−i3i3000000000000000
χ7644-4-4-2-2424-22-4-422-21-2-20-1-122-2-22212i3−2i3-44001-1-11002i3−2i300−i3i3−i3−i3i3i30000002-2−2i32i3000000002-2000000000000000000-11i3−i3000000000000000
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χ784-44-444-242-44-22-4-4-44-2-204-4-2-22222-4000000-2-22200000000000000000000000023−2300000000000000000023−2300000000000000000000000
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χ804-44-44-24-2-4-444-42-42-24-20-224-2-422-42000000-2-2220000000000000000−2i32i3000000000000000000000−2i32i30000000000000000000000000000
χ814-44-44-24-2-4-444-42-42-24-20-224-2-422-42000000-2-22200000000000000002i3−2i30000000000000000000002i3−2i30000000000000000000000000000
χ824-44-44-2-2-22-44-222-42-2-210-22-212-1-12200000011-1-100003i−3i003i−3i3i−3i0000−2i32i300000023−230000000000000i3−i3000−3300000000000000000000000
χ834-44-44-2-2-22-44-222-42-2-210-22-212-1-12200000011-1-100003i−3i003i−3i3i−3i00002i3−2i3000000−23230000000000000−i3i30003−300000000000000000000000
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χ854-44-44-2-2-22-44-222-42-2-210-22-212-1-12200000011-1-10000−3i3i00−3i3i−3i3i00002i3−2i300000023−230000000000000−i3i3000−3300000000000000000000000
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χ884-4-44444-4-4-4-4-4444-44440-44-4-4-4-444-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-42-4-42-244-44-2-20-442222-2-2-4000000-22-2200000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ904-4-4444-2-42-4-42-244-44-2-20-442222-2-2-4000000-22-22000000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ914-4-444-242-4-4-4-44-242-24-202-2-42-42-242000000-22-2200000000000000000000000000000000000000000000000000000000000000023−230000
χ924-4-444-242-4-4-4-44-242-24-202-2-42-42-242000000-22-22000000000000000000000000000000000000000000000000000000000000000−23230000
χ934-4-44-244-4-422-444-2-4-2-2402-22-42-44-22000000-22-22000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ944-4-44-244-4-422-444-2-4-2-2402-22-42-44-22000000-22-220000000000000000000000000000000000−232323−230000000000000000000000000000000
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
χ9788-8-88-4-44-48-8444-8-4-4-420444-2-42-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-4-444444-42220-2-2-2-222-2-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-4-444444-42220-2-2-2-222-2-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-4844-4-44-84-8-42-40-442-4-244-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48-4-84-48-84442-4-402-2-4-44444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-444-4-4444422202-222-2-2-2-2-2000000-1-11100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-444-4-4444422202-222-2-2-2-2-2000000-1-1110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-444-8-84-4-484-4-4204-44-24-22-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-84444-48-4-8-42-404-4-24-24-4240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-844-88-4-442-4-40-224444-4-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-4-4-442220-22-2-2-2-222-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-4-4-442220-22-2-2-2-222-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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