Finite Group Databasebeta

← Group #13172037

Character table — Group #13172037

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666233366666666666666666224412121212366666666666644446666121212121212121212121212121212121212446612121212121212121212244441212121212126121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-1111111-1-11111111111111111111-1-1-111-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1-111-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-1-1-11111111111111111-1-1-1-1-1111-1-11111-1-1-111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11111-11-1-1-111-1-111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-11-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-11-1-111-1-1-1-11-11-1-11111-11-1-11
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-1-1-1-1111-1-11-1-1-1-1-1111-111-1
χ111111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-111-1-11111-1-11111-1-111-1-1-1-11111-1-111-1-1-11-1-111-1-1-1111-11111-1-1-1-111-1
χ121111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-1-111111-1-1-1-111-1-111-1-1-1-11111-1-111-111-1-1-1-1-11111-1-1111-1-1-1-111-1-11
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11111111-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1111-1-1-1-111-11-1
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11111111-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111-111-1-111-1111-11111-1-1-1-11-11
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1111111-1-111-1-1-1-1111111-1-11-1-111111-1-11-1-11-1-1-1-1-1111-11-11
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1111-111-1-111-1-11-11-1-11111-11-11-1
χ17222222-12-12-122-12222-1-1222222-12222-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-1022222-1-122-1-10000000000000000-1-1-1-122-1-1-1-1-1-12020000-1-100-10000
χ18222222-12-12-122-12222-1-1222222-12222-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-10-22-222-1-122110000000000000000-1-1-11-2-2-1-11111-20-20000110010000
χ19222222-12-12-122-12222-1-1222222-12222-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-102-22-2-211-2-2-1-10000000000000000111-12211-1-1-1-1-20-20000110010000
χ20222222-12-12-122-12222-1-1222222-12222-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2-2-211-2-21100000000000000001111-2-21111112020000-1-100-10000
χ21222222-12-12-122-122-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1222000000-111111-1-1-1111102-2-222-1-1-2-2-1-10000000000000000-1-111-2211-1-111-2020000-1-10010000
χ22222222-12-12-122-122-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1222000000-111111-1-1-111110-2-2222-1-1-2-2110000000000000000-1-11-12-21111-1-120-200001100-10000
χ23222222-12-12-122-122-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-12-2-2000000-111111-1-1-11111022-2-2-21122-1-1000000000000000011-11-22-1-1-1-11120-200001100-10000
χ24222222-12-12-122-122-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-12-2-2000000-111111-1-1-111110-222-2-2112211000000000000000011-1-12-2-1-111-1-1-2020000-1-10010000
χ2522222-1222-12-122-122-12-122-1-1-1-12-1-1-1-1-1-122-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1-12020-1-122-1-100-1-12222-1-1-1-1-1-1-1-122-1-12000-1-1000002000-1-100-1-100000
χ2622222-1222-12-122-122-12-122-1-1-1-12-1-1-1-1-1-122-1-122-2-21111-1222-1-1-1-1-1-1-1-1-1-2020-1-122-1-10011-2-2-2-211111111-2-2-1-12000-1-100000-200011001100000
χ2722222-1222-12-122-122-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-1-120-2011-2-21100-1-12222-1-1-1-1-1-1-1-1-2-211-20001100000-200011001100000
χ2822222-1222-12-122-122-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-2-2-21111-1222-1-1-1-1-1-1-1-1-1-20-2011-2-2110011-2-2-2-2111111112211-200011000002000-1-100-1-100000
χ2922222-1222-12-122-12-2-12-1-2-211-1-121111-1-122-1-12222-1-1-1-1-1-2-2-211-1-1-11111-20-20-1-12211001122-2-2-1-1-1-1111122-1-1-20001100000-20001100-1-100000
χ3022222-1222-12-122-12-2-12-1-2-211-1-121111-1-122-1-122-2-21111-1-2-2-211-1-1-1111120-20-1-1221100-1-1-2-2221111-1-1-1-1-2-2-1-1-200011000002000-1-1001100000
χ3122222-1222-12-122-12-2-12-1-2-211-1-121111-1-122-1-1-2-222-1-1-1-1-1-2-2-211-1-1-11111-202011-2-2-1-1001122-2-2-1-1-1-11111-2-2112000-1-1000002000-1-1001100000
χ3222222-1222-12-122-12-2-12-1-2-211-1-121111-1-122-1-1-2-2-2-21111-1-2-2-211-1-1-11111202011-2-2-1-100-1-1-2-2221111-1-1-1-122112000-1-100000-20001100-1-100000
χ332222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100222222-12-1-122-1-1-1-1-1-1-122020000002222-1-1-1-1-1-1-1-1-1-1-1-1000002-1-100-1-1-1-1000220000000-1-100
χ342222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100222222-12-1-122-1-1-1-1-1-1-12-20-2000000-2-222-1-1-1-1-1-1-1-1-1-1-1-100000-211001111000-2-200000001100
χ352222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-1-220200000022-2-2111111111111000002-1-100-1-1-1-1000-2-200000001100
χ362222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-1-2-20-2000000-2-2-2-211111111111100000-211001111000220000000-1-100
χ372222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100222222-1-211-2-2-1-1-11111-220-200000022-2-2-1-111-1-1-1-1111100000-21-100-1-111000-220000000-1100
χ382222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100222222-1-211-2-2-1-1-11111-2-202000000-2-2-2-2-1-111-1-1-1-11111000002-110011-1-10002-200000001-100
χ392222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100-2-2-2-2-2-2-1-211-2-2-1-1-11111220-2000000222211-1-11111-1-1-1-100000-21-100-1-1110002-200000001-100
χ402222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100-2-2-2-2-2-2-1-211-2-2-1-1-111112-202000000-2-22211-1-11111-1-1-1-1000002-110011-1-1000-220000000-1100
χ412-2-22222-2-222-22-2-2-2022200002-2-20000-2-22-22-22-22i−2i2i2i−2i−2i2000002-2-2000000002-22-20000002i−2i002i2i−2i−2i00002i−2i2-200000000000000000002i−2i00000
χ422-2-22222-2-222-22-2-2-2022200002-2-20000-2-22-22-22-2−2i2i−2i−2i2i2i2000002-2-2000000002-22-2000000−2i2i00−2i−2i2i2i0000−2i2i2-20000000000000000000−2i2i00000
χ432-2-22222-2-222-22-2-2-2022200002-2-20000-2-22-22-2-222i−2i2i2i−2i−2i2000002-2-200000000-22-220000002i−2i002i2i−2i−2i0000−2i2i-220000000000000000000−2i2i00000
χ442-2-22222-2-222-22-2-2-2022200002-2-20000-2-22-22-2-22−2i2i−2i−2i2i2i2000002-2-200000000-22-22000000−2i2i00−2i−2i2i2i00002i−2i-2200000000000000000002i−2i00000
χ452-2-222-12-2-2-1212-21-20-12-100−i3i3-11-2−i3−i3i3i3112-2-112-22i−2i−i−iii-1000−i3i3-111−i3−i3i3i30000-112-2−i3i3003−32i−2i00−i−iii33−3−32i−2i-110000−i3i30000000003−300−ii00000
χ462-2-222-12-2-2-1212-21-20-12-100−i3i3-11-2−i3−i3i3i3112-2-112-2−2i2iii−i−i-1000−i3i3-111−i3−i3i3i30000-112-2−i3i300−33−2i2i00ii−i−i−3−333−2i2i-110000−i3i3000000000−3300i−i00000
χ472-2-222-12-2-2-1212-21-20-12-100−i3i3-11-2−i3−i3i3i3112-2-11-222i−2i−i−iii-1000−i3i3-111−i3−i3i3i300001-1-22i3−i3003−32i−2i00−i−iii33−3−3−2i2i1-10000i3−i3000000000−3300i−i00000
χ482-2-222-12-2-2-1212-21-20-12-100−i3i3-11-2−i3−i3i3i3112-2-11-22−2i2iii−i−i-1000−i3i3-111−i3−i3i3i300001-1-22i3−i300−33−2i2i00ii−i−i−3−3332i−2i1-10000i3−i30000000003−300−ii00000
χ492-2-222-12-2-2-1212-21-20-12-100i3−i3-11-2i3i3−i3−i3112-2-112-22i−2i−i−iii-1000i3−i3-111i3i3−i3−i30000-112-2i3−i300−332i−2i00−i−iii−3−3332i−2i-110000i3−i3000000000−3300−ii00000
χ502-2-222-12-2-2-1212-21-20-12-100i3−i3-11-2i3i3−i3−i3112-2-112-2−2i2iii−i−i-1000i3−i3-111i3i3−i3−i30000-112-2i3−i3003−3−2i2i00ii−i−i33−3−3−2i2i-110000i3−i30000000003−300i−i00000
χ512-2-222-12-2-2-1212-21-20-12-100i3−i3-11-2i3i3−i3−i3112-2-11-222i−2i−i−iii-1000i3−i3-111i3i3−i3−i300001-1-22−i3i300−332i−2i00−i−iii−3−333−2i2i1-10000−i3i30000000003−300i−i00000
χ522-2-222-12-2-2-1212-21-20-12-100i3−i3-11-2i3i3−i3−i3112-2-11-22−2i2iii−i−i-1000i3−i3-111i3i3−i3−i300001-1-22−i3i3003−3−2i2i00ii−i−i33−3−32i−2i1-10000−i3i3000000000−3300−ii00000
χ5344444-2-24-2-2-2-24-2-244-2-2144-2-2-2-2-2-2-2-2-211-2-21-2440000001-2-2-21111111110040-2-2-2-2-2-200000000000000000011-20001100000000000000000000
χ5444444-2-24-2-2-2-24-2-244-2-2144-2-2-2-2-2-2-2-2-211-2-21-2-4-40000001-2-2-211111111100-40222222000000000000000000-1-12000-1-100000000000000000000
χ5544444-2-24-2-2-2-24-2-24-4-2-21-4-422-2-2-2222211-2-21-2440000001222-1-1111-1-1-1-100-40-2-2-2-222000000000000000000112000-1-100000000000000000000
χ5644444-2-24-2-2-2-24-2-24-4-2-21-4-422-2-2-2222211-2-21-2-4-40000001222-1-1111-1-1-1-100402222-2-2000000000000000000-1-1-20001100000000000000000000
χ574444-24-2-2-24-24-2-24-24-21-2-2-244-2-21-2-2-2-2-2-211-2-2000000001-211-2-211111110404000000-2-20000000000000000000-2-2-20011110000000000000000
χ584444-24-2-2-24-24-2-24-24-21-2-2-244-2-21-2-2-2-2-2-211-2-2000000001-211-2-211111110-40-400000022000000000000000000022200-1-1-1-10000000000000000
χ594444-24-2-2-24-24-2-24-2-4-21-222-4-4-2-212222-2-211-2-20000000012-1-122111-1-1-1-1040-4000000-2-2000000000000000000022-20011-1-10000000000000000
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χ7244-4-4-24-2-2-2-42422-420-21-2−2i32i3002-21−2i32i3−2i32i3-22-1-1220000000010i3−i300-11-1i3−i3i3−i3000000000023−23000000000000000000000000−333i−3i0000000000000000
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χ7744-4-4-2-24-242-4-22-42201-2-2−2i32i300-11-2i3−i3i3−i3-22222-10000−2323−232310−2i32i300-11-1i3−i3i3−i30000000000000000003−33−3−3i3i−3i3i000000000000000000000000000000
χ7844-4-4-2-24-242-4-22-42201-2-22i3−2i300-11-2−i3i3−i3i3-22222-1000023−2323−23102i3−2i300-11-1−i3i3−i3i3000000000000000000−33−33−3i3i−3i3i000000000000000000000000000000
χ7944-4-4-2-24-242-4-22-42201-2-22i3−2i300-11-2−i3i3−i3i3-22222-10000−2323−2323102i3−2i300-11-1−i3i3−i3i30000000000000000003−33−33i−3i3i−3i000000000000000000000000000000
χ804-44-4444-4-4-4-4-4-444404440000-4-4-40000-44-44-4400000000400000-4-44000000000000000000000000000000000000000000000000000000000000
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χ874-44-4-2-242-42-4224-2-201-2-20000-1-123-3-332-22-2210000−2i32i32i3−2i3100000-1-113-3-330000000000000000−2i32i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000
χ884-44-4-2-242-42-4224-2-201-2-20000-1-123-3-332-22-22100002i3−2i3−2i32i3100000-1-113-3-3300000000000000002i3−2i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000
χ894-44-4-2-242-42-4224-2-201-2-20000-1-12-333-32-22-2210000−2i32i32i3−2i3100000-1-11-333-300000000000000002i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000
χ904-44-4-2-242-42-4224-2-201-2-20000-1-12-333-32-22-22100002i3−2i3−2i32i3100000-1-11-333-30000000000000000−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000
χ914-4-4444-2-424-2-442-4-404-2-200004-42000022-22-2-44-4000000-200000-222000000004-4-2200000000000000000000-2200000000000000000000000000
χ924-4-4444-2-424-2-442-4-404-2-200004-42000022-22-2-4-44000000-200000-22200000000-442-2000000000000000000002-200000000000000000000000000
χ934-4-444-2-2-42-2-22422-40-2-2100−2i32i3-222−2i3−2i32i32i3-1-1-22124-40000001000i3−i31-1-1i3i3−i3−i30000-22-22−2i32i30000000000000000001-10000i3−i300000000000000000000
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χ964-4-444-2-2-42-2-22422-40-2-21002i3−2i3-2222i32i3−2i3−2i3-1-1-2212-440000001000−i3i31-1-1−i3−i3i3i300002-22-2−2i32i3000000000000000000-110000i3−i300000000000000000000
χ974-4-44-2442-444-4-2-4-420-2-240000-2220000-4-4-2242004i−4i4i4i−4i−4i-200000-222000000000000000000−2i2i00−2i−2i2i2i0000000000000000000000000000000000
χ984-4-44-2442-444-4-2-4-420-2-240000-2220000-4-4-224200−4i4i−4i−4i4i4i-200000-2220000000000000000002i−2i002i2i−2i−2i0000000000000000000000000000000000
χ994-4-44-2-242-4-242-2-42201-2-200−2i32i31-12i3i3−i3−i322-22-2-1004i−4i−2i−2i2i2i1000−2i32i31-1-1i3i3−i3−i300000000000023−23−2i2i00ii−i−i−3−333000000000000000000000000000000
χ1004-4-44-2-242-4-242-2-42201-2-200−2i32i31-12i3i3−i3−i322-22-2-100−4i4i2i2i−2i−2i1000−2i32i31-1-1i3i3−i3−i3000000000000−23232i−2i00−i−iii33−3−3000000000000000000000000000000
χ1014-4-44-2-242-4-242-2-42201-2-2002i3−2i31-12−i3−i3i3i322-22-2-1004i−4i−2i−2i2i2i10002i3−2i31-1-1−i3−i3i3i3000000000000−2323−2i2i00ii−i−i33−3−3000000000000000000000000000000
χ1024-4-44-2-242-4-242-2-42201-2-2002i3−2i31-12−i3−i3i3i322-22-2-100−4i4i2i2i−2i−2i10002i3−2i31-1-1−i3−i3i3i300000000000023−232i−2i00−i−iii−3−333000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4-4-4222222222222200000000-1-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4-82224444222-2-2-2-222222200000000-14-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ10588-8-88-4-48-444-4-844-80-4-4200004-4-400002-244-2400000000200000-22-2000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-4-444-444440222−4i34i300-2222i3−2i32i3−2i32-2-2-2-2-200000000-102i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-4-444-4444402224i3−4i300-222−2i32i3−2i32i32-2-2-2-2-200000000-10−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-84444-8-4-480-4-4200004440000-224-4-2-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-444-84-84-48-40-42-4000044-200004-4-224-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444444-4-4-402220000-2-2-26-6-66-22-22-2200000000-10000011-1-333-300000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4444444-4-4-402220000-2-2-2-666-6-22-22-2200000000-10000011-13-3-3300000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-4448-4-8-44-840-42-40000-44-20000442-2-44000000002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444-4-44-4444022200−4i34i32-2-22i32i3−2i3−2i3-2-22-22-200000000-10002i3−2i3-111−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444-4-44-44440222004i3−4i32-2-2−2i3−2i32i32i3-2-22-22-200000000-1000−2i32i3-111i3i3−i3−i300000000000000000000000000000000000000000000000000000000

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