Finite Group Databasebeta

← Group #13168748

Character table — Group #13168748

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212224466666666121212121212121244121212126666666612121212121212122444412121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1111111-1-1-1-11111111111111-1-1-11111-11-1-11111-1-1-11-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-11-1-11-1-111-1-1-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111-111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1111111111-11-1-1-1-1-1-1111-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-11-1-11-1-111-1-1-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-11111-1-1-1-1-1-1111111-1111-1-1-1-11-111-1-1-1-1-1-1-11-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-11111-1-1111111-111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1111111-1-1111111-1-1-1-111-1-11-11111-1-11-1-1-11-1-111-1-11-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111-11-111-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1111111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-11111-1-111-11-111-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-1-1-1-1-1111111111111-1-111-11-1-1-1-1111-1-1-11-1-111-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1111111-1-111-111-1-1-1-1-1-111-111-1
χ17222222-122-1-12222-1-1-122-1-122-1-12-1-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-10222000000-1-12222-1-12200000002-1-10000-1-1-1-1-1-1-1-1202000000-1-1-1000
χ18222222-122-1-12222-1-1-122-1-122-1-12-1-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-10-22-200000011-2-222-1-1220000000-21100001-111-1-1-1-1-20-2000000111000
χ19222222-122-1-12222-1-1-122-1-122-1-12-1-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-102-22000000-1-122-2-211-2-200000002-1-10000-11-1-11111-20-2000000111000
χ20222222-122-1-12222-1-1-122-1-122-1-12-1-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-200000011-2-2-2-211-2-20000000-211000011111111202000000-1-1-1000
χ21222222-122-1-12222-1-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-11-2-2-21111111102-2-2000000-1-1-2-222-1-1-2-200000002-1-100001111-1-111-202000000-1-11000
χ22222222-122-1-12222-1-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-11-2-2-2111111110-2-22000000112222-1-1-2-20000000-2110000-11-1-1-1-11120-200000011-1000
χ23222222-122-1-12222-1-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-11-2-2-211111111022-2000000-1-1-2-2-2-2112200000002-1-100001-11111-1-120-200000011-1000
χ24222222-122-1-12222-1-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-11-2-2-2111111110-2220000001122-2-211220000000-2110000-1-1-1-111-1-1-202000000-1-11000
χ2522222-12-12222-1-1222-1-122-1-1-12-1-1-12222200-1-1-1-12-1-1-122-1-1-1-1-1-122022222-1-122-1-1000000000000-1-1-1-1-1-1-1-120-1-100000200200-1-1000-100
χ2622222-12-12222-1-1222-1-122-1-1-12-1-1-12222200-1-1-1-12-1-1-122-1-1-1-1-1-12-20-22222-1-1-2-211000000000000-1111-1-1-1-1-201100000-200-20011000100
χ2722222-12-12222-1-1222-1-122-1-1-12-1-1-1222-2-200-1-1-1-12-1-1-122-1-1-1-1-1-1-2202-2-2-2-21122-1-10000000000001-1-1-1111120-1-100000-200-20011000100
χ2822222-12-12222-1-1222-1-122-1-1-12-1-1-1222-2-200-1-1-1-12-1-1-122-1-1-1-1-1-1-2-20-2-2-2-2-211-2-21100000000000011111111-201100000200200-1-1000-100
χ2922222-12-12222-1-1222-1-1-22-1-1-12-1-1-12-2-22200-1-1-1-1-2111-2-2111111-220-222-2-2-1-122110000000000001-1-1-1-1-111-201100000200-20011000-100
χ3022222-12-12222-1-1222-1-1-22-1-1-12-1-1-12-2-22200-1-1-1-1-2111-2-2111111-2-20222-2-2-1-1-2-2-1-10000000000001111-1-11120-1-100000-200200-1-1000100
χ3122222-12-12222-1-1222-1-1-22-1-1-12-1-1-12-2-2-2-200-1-1-1-1-2111-2-2111111220-2-2-222112211000000000000-1-1-1-111-1-1-201100000-200200-1-1000100
χ3222222-12-12222-1-1222-1-1-22-1-1-12-1-1-12-2-2-2-200-1-1-1-1-2111-2-21111112-202-2-22211-2-2-1-1000000000000-111111-1-120-1-100000200-20011000-100
χ332222-1222-122-122-12-12-12-12-1-1-12-12-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12020-1-1-1-1220000-1-122-1-122-1-1-1-12000-1-1-1-10200-1-1-1-100020-1-100000000
χ342222-1222-122-122-12-12-12-12-1-1-12-12-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-120-20-1-1-1-122000011-2-211-2-211112000-1-1-1-10-2001111000-201100000000
χ352222-1222-122-122-12-12-12-12-1-1-12-12-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-20201111-2-20000-1-122-1-1-2-21111-200011110200-1-1-1-1000-201100000000
χ362222-1222-122-122-12-12-12-12-1-1-12-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-20-201111-2-2000011-2-21122-1-1-1-1-200011110-200111100020-1-100000000
χ372222-1222-122-122-12-12-1-2-12-1-1-12-12-1112222-1-1-1-1-2-21111-2-21111-20-20-1-111220000-1-1221122-1-1-1-1-2000-1-1110-200-1-111000-201100000000
χ382222-1222-122-122-12-12-1-2-12-1-1-12-12-11122-2-2-1-1-1-1-2-21111-2-21111-2020-1-11122000011-2-2-1-1-2-21111-2000-1-111020011-1-100020-1-100000000
χ392222-1222-122-122-12-12-1-2-12-1-1-12-12-111-2-222-1-1-1-1-2-21111-2-2111120-2011-1-1-2-20000-1-12211-2-21111200011-1-10-200-1-11100020-1-100000000
χ402222-1222-122-122-12-12-1-2-12-1-1-12-12-111-2-2-2-2-1-1-1-1-2-21111-2-21111202011-1-1-2-2000011-2-2-1-122-1-1-1-1200011-1-1020011-1-1000-201100000000
χ4122-2-2222-222-2-22-2-2-22220-2-2-2-2222-2-2002-22i−2i2-2-2200000000000000002-2002-200002i−2i2i−2i002i−2i2i2i−2i−2i00002-20000002i−2i00000000000000000
χ4222-2-2222-222-2-22-2-2-22220-2-2-2-2222-2-2002-2−2i2i2-2-2200000000000000002-2002-20000−2i2i−2i2i00−2i2i−2i−2i2i2i00002-2000000−2i2i00000000000000000
χ4322-2-2222-222-2-22-2-2-22220-2-2-2-2222-2-200-222i−2i2-2-220000000000000000-2200-2200002i−2i2i−2i00−2i2i−2i−2i2i2i0000-220000002i−2i00000000000000000
χ4422-2-2222-222-2-22-2-2-22220-2-2-2-2222-2-200-22−2i2i2-2-220000000000000000-2200-220000−2i2i−2i2i002i−2i2i2i−2i−2i0000-22000000−2i2i00000000000000000
χ4522-2-2-122-2-12-212-21-2-12-101-211-12-1-21−i3i32-22i−2i-111-100−i3i3−i3i300−i3−i3i3i30000-11−i3i32-20000−ii2i−2i3−32i−2i−i−iii0000-11−i3i30000−ii3−3000003−300000000
χ4622-2-2-122-2-12-212-21-2-12-101-211-12-1-21−i3i32-2−2i2i-111-100−i3i3−i3i300−i3−i3i3i30000-11−i3i32-20000i−i−2i2i−33−2i2iii−i−i0000-11−i3i30000i−i−3300000−3300000000
χ4722-2-2-122-2-12-212-21-2-12-101-211-12-1-21−i3i3-222i−2i-111-100−i3i3−i3i300−i3−i3i3i300001-1i3−i3-220000−ii2i−2i3−3−2i2iii−i−i00001-1i3−i30000−ii3−300000−3300000000
χ4822-2-2-122-2-12-212-21-2-12-101-211-12-1-21−i3i3-22−2i2i-111-100−i3i3−i3i300−i3−i3i3i300001-1i3−i3-220000i−i−2i2i−332i−2i−i−iii00001-1i3−i30000i−i−33000003−300000000
χ4922-2-2-122-2-12-212-21-2-12-101-211-12-1-21i3−i32-22i−2i-111-100i3−i3i3−i300i3i3−i3−i30000-11i3−i32-20000−ii2i−2i−332i−2i−i−iii0000-11i3−i30000−ii−3300000−3300000000
χ5022-2-2-122-2-12-212-21-2-12-101-211-12-1-21i3−i32-2−2i2i-111-100i3−i3i3−i300i3i3−i3−i30000-11i3−i32-20000i−i−2i2i3−3−2i2iii−i−i0000-11i3−i30000i−i3−3000003−300000000
χ5122-2-2-122-2-12-212-21-2-12-101-211-12-1-21i3−i3-222i−2i-111-100i3−i3i3−i300i3i3−i3−i300001-1−i3i3-220000−ii2i−2i−33−2i2iii−i−i00001-1−i3i30000−ii−33000003−300000000
χ5222-2-2-122-2-12-212-21-2-12-101-211-12-1-21i3−i3-22−2i2i-111-100i3−i3i3−i300i3i3−i3−i300001-1−i3i3-220000i−i−2i2i3−32i−2i−i−iii00001-1−i3i30000i−i3−300000−3300000000
χ5344444-2-2-24-2-24-2-24-2-21-24-21-2-2-21-21-24400001111-2-2-2-2-2-21111110404000000-2-2-2-20000000000000-2110000-20110000000000000000000
χ5444444-2-2-24-2-24-2-24-2-21-24-21-2-2-21-21-24400001111-2-2-2-2-2-21111110-40-4000000222200000000000002-1-1000020-1-10000000000000000000
χ5544444-2-2-24-2-24-2-24-2-21-2-4-21-2-2-21-21-2-4-400001111222222-1-1-1-1-1-1040-4000000-2-2220000000000000-211000020-1-10000000000000000000
χ5644444-2-2-24-2-24-2-24-2-21-2-4-21-2-2-21-21-2-4-400001111222222-1-1-1-1-1-10-40400000022-2-200000000000002-1-10000-20110000000000000000000
χ574444-24-24-2-2-2-244-2-21-2-241-2-2-21-2-2-21-2-200441111-24-2-211-2-2111100400000000000-2-2-2-2-2-2000000000000000-2001111000000000000000
χ584444-24-24-2-2-2-244-2-21-2-241-2-2-21-2-2-21-2-200-4-41111-24-2-211-2-2111100-400000000000222222000000000000000200-1-1-1-1000000000000000
χ594444-24-24-2-2-2-244-2-21-2-2-41-2-2-21-2-2-2122004411112-422-1-122-1-1-1-100-400000000000-2-2-2-22200000000000000020011-1-1000000000000000
χ604444-24-24-2-2-2-244-2-21-2-2-41-2-2-21-2-2-212200-4-411112-422-1-122-1-1-1-1004000000000002222-2-2000000000000000-200-1-111000000000000000
χ614444-2-24-2-244-2-2-2-24-2-214-2-211-2-21-2-2-2-2440011114-211-2-2-2-211114000-2-2-2-2-2-20000000000000000-2000111100000000000000000000000
χ624444-2-24-2-244-2-2-2-24-2-214-2-211-2-21-2-2-2-2-4-40011114-211-2-2-2-21111-400022222200000000000000002000-1-1-1-100000000000000000000000
χ634444-2-24-2-244-2-2-2-24-2-21-4-2-211-2-21-2-22244001111-42-1-12222-1-1-1-1-4000-2-222-2-20000000000000000200011-1-100000000000000000000000
χ644444-2-24-2-244-2-2-2-24-2-21-4-2-211-2-21-2-222-4-4001111-42-1-12222-1-1-1-1400022-2-2220000000000000000-2000-1-11100000000000000000000000
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χ6644-4-444-2-44-22-44-4-42-2-24022-4-4-2-24220000−4i4i-222-200000000000000000000000000−4i4i2i−2i000000000000000000002i−2i00000000000000000
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χ7444-4-4-2-242-24-42-222-4-2-21022-1-1-2-2122−2i32i3-44001-1-1100i3−i3−2i32i300i3i3−i3−i300002-22i3−2i32-200000000000000000000-11−i3i300000000000000000000000
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χ814-44-44-24-2-4-4-4-422444-2-20-4-2-22-42224000000-2-222000000000000000000000000−23230000000000000000000000−23230000000000000000000
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χ884-4-44444-4-4-444-44-4-444404-4-44-4-4-44-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-42-24-44-42-2-240-22-4422-4-22000000-22-2200000000000000000000000000000000000000000000000000000000000000023−230000
χ904-4-4444-2-4-42-24-44-42-2-240-22-4422-4-22000000-22-22000000000000000000000000000000000000000000000000000000000000000−23230000
χ914-4-444-242-4-4442-2-4-44-2-20422-2-422-2-4000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ924-4-444-242-4-4442-2-4-44-2-20422-2-422-2-4000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ934-4-44-244-42-44-2-442-4-24-20-2-42-22-4242000000-22-22000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ944-4-44-244-42-44-2-442-4-24-20-2-42-22-4242000000-22-220000000000000000000000000000000000−232323−230000000000000000000000000000000
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
χ9788-8-88-4-448-44-8-44-84-42-404-244-42-4-240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-4-444-44442220-2-2-2-2222-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-4-444-44442220-2-2-2-2222-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-484444-8-8-4-42-4-40-2-4-44-2444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48-44-8-8444-48-4-4204-42-244-24-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-4444444-4-42220-222-2-2-2-2-22000000-1-1110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-4444444-4-42220-222-2-2-2-2-22000000-1-111000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-44-84-484-4-84-42-40-4-24-44-24240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-844-4-4-88442-4-40244-4-244-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-88-44-44-8-4-420-44-2244-2-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-4-44-44422202-2-22-2-2-22-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-4-44-44422202-2-22-2-2-22-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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