Finite Group Databasebeta

← Group #13170807

Character table — Group #13170807

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order122233366666666633346666666661212224444366612121212121212121212121244442446666661212121212121212121222441212121266666121212121212121212121244466121212122212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111111111-111111111-1-11111-1-1-1-1-1-1111111111-11-11111-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-1-111-1-111111-1-111111-1-1-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-11-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-11-111-1-1-1-1-1-1-1-1111-1-1-1-1111-11
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-11-11-1-1-1-1111111-1-1111111-1-1-1-1-1-11-1-1111-11-1-1111111-1-1111-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-11-1-1-111-1-111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-1111111111111-111-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-1-1-111-1-1-1-1-1-11111-111-1-11-11-1-111-1-1111-11-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-1-1-111-1-111-1-1-1-111111-1-1-1-1-1-1-111-1-1-111-1-11111-1-11-11
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-11-1-1-1-1-1-11111-11111-1-111-11-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1111111-1-111-11111-1-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11111111-1-111-111-1-11111111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-111-1-1-1-111111-1-111-11-111-1-111-1-11-11-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1111111111-1-11111111-1-1-1-111-1-1-111-1-111-1-1-1-11
χ17222222-122-12-1-1222-12-12-12-1-12-12-1-122002222-1-1-1-1-1222-1-1-1-1-1-1-1-10000202000022-1-1-1-100222222000000-100-1-1-10200-1-1-1-1-1-1002-1-1000000-100
χ18222222-122-12-1-1222-12-12-12-1-12-12-1-1220022-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1000020-2000022-1-1110022-2-2-2-2000000-100-1-110-200-1-1111100-211000000100
χ19222222-122-12-1-1222-12-12-12-1-12-12-1-12200-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-10000-2020000-2-211-1-100-2-222-2-200000010011-1020011-1-1-1-100-211000000100
χ20222222-122-12-1-1222-12-12-12-1-12-12-1-12200-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10000-20-20000-2-2111100-2-2-2-2220000001001110-200111111002-1-1000000-100
χ21222222-122-12-1-1222-12-1-2-12-1-12-12-1-1-2-2002222-1-1-1-11-2-2-2111111110000-20-20000-2-2-1-1-1-1002222220000001001110-200-1-1-1-11100-2-1-1000000100
χ22222222-122-12-1-1222-12-1-2-12-1-12-12-1-1-2-20022-2-2-1-1-1-11-2-2-2111111110000-2020000-2-2-1-1110022-2-2-2-200000010011-10200-1-111-1-100211000000-100
χ23222222-122-12-1-1222-12-1-2-12-1-12-12-1-1-2-200-2-222-1-1-1-11-2-2-211111111000020-200002211-1-100-2-222-2-2000000-100-1-110-20011-1-11100211000000-100
χ24222222-122-12-1-1222-12-1-2-12-1-12-12-1-1-2-200-2-2-2-2-1-1-1-11-2-2-2111111110000202000022111100-2-2-2-222000000-100-1-1-102001111-1-100-2-1-1000000100
χ2522222-122-12-1222-122-1-122-1-12-1-1-1-12-1-1222200-1-1-1-122-1-122-1-1-1-1-1-1222222022-1-1-1-12200-1-1-1-1000000-1-1-1-12-1-1-1-1020-1-1-1-1000002000-1-10000000
χ2622222-122-12-1222-122-1-122-1-12-1-1-1-12-1-122-2-200-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-2-22022-1-111-2-200-1-1110000001111-2-1-111020-1-11100000-2000110000000
χ2722222-122-12-1222-122-1-122-1-12-1-1-1-12-1-1-2-22200-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-22-20-2-211-1-1220011-1-10000001111211-1-10-2011-1-100000-2000110000000
χ2822222-122-12-1222-122-1-122-1-12-1-1-1-12-1-1-2-2-2-200-1-1-1-122-1-122-1-1-1-1-1-12222-2-20-2-21111-2-2001111000000-1-1-1-1-211110-201111000002000-1-10000000
χ2922222-122-12-1222-122-1-1-22-1-12-1-1-1-1211222200-1-1-1-1-2-211-2-21111112222-2-2022-1-111220011-1-1000000-1-1-1-1-2-1-1110-2011-1-100000-2000110000000
χ3022222-122-12-1222-122-1-1-22-1-12-1-1-1-121122-2-200-1-1-1-1-2-211-2-2111111-2-2-2-22-2022-1-1-1-1-2-200111100000011112-1-1-1-10-201111000002000-1-10000000
χ3122222-122-12-1222-122-1-1-22-1-12-1-1-1-1211-2-22200-1-1-1-1-2-211-2-2111111-2-2-2-2-220-2-211112200-1-1-1-10000001111-21111020-1-1-1-1000002000-1-10000000
χ3222222-122-12-1222-122-1-1-22-1-12-1-1-1-1211-2-2-2-200-1-1-1-1-2-211-2-21111112222220-2-211-1-1-2-200-1-111000000-1-1-1-1211-1-1020-1-11100000-2000110000000
χ332222-122-122222-12-1-1-122-1-12-1-12-12-122220022-1-1-1-12-1-1-1-1-122-1-1-1-10000022-1-1220000222200-1-1002200000-1-1002-1-1-1-100-1-1-1-12000000-1-1000-10
χ342222-122-122222-12-1-1-122-1-12-1-12-12-1222200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1000002-2-1-1220000-2-222001100-2-200000-1-100-2-11-1-1001111-20000001100010
χ352222-122-122222-12-1-1-122-1-12-1-12-12-122-2-20022-1-1-1-12-1-1-1-1-122-1-1-1-100000-2211-2-2000022-2-200-1-100-2-200000110021-11100-1-1-1-1-20000001100010
χ362222-122-122222-12-1-1-122-1-12-1-12-12-122-2-200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-100000-2-211-2-20000-2-2-2-200110022000001100-211110011112000000-1-1000-10
χ372222-122-122222-12-1-1-12-2-1-12-1-12-12-1-2-2220022-1-1-1-1-211111-2-2111100000-2-2-1-122000022-2-200-1-1002200000-1-100-2111100-1-111-2000000-1-100010
χ382222-122-122222-12-1-1-12-2-1-12-1-12-12-1-2-22200-2-2-1-1-1-1-211111-2-2111100000-22-1-1220000-2-2-2-2001100-2-200000-1-10021-1110011-1-1200000011000-10
χ392222-122-122222-12-1-1-12-2-1-12-1-12-12-1-2-2-2-20022-1-1-1-1-211111-2-21111000002-211-2-20000222200-1-100-2-2000001100-2-11-1-100-1-111200000011000-10
χ402222-122-122222-12-1-1-12-2-1-12-1-12-12-1-2-2-2-200-2-2-1-1-1-1-211111-2-21111000002211-2-20000-2-222001100220000011002-1-1-1-10011-1-1-2000000-1-100010
χ4122-2-2222-222-2-2-22-2-22220-2-2-2222-2-2-20000002i−2i2-2-220000000000002i2i−2i−2i000000000002i−2i00002i−2i00002i2i−2i−2i0000000000002i−2i000000000002-2000
χ4222-2-2222-222-2-2-22-2-22220-2-2-2222-2-2-20000002i−2i2-2-22000000000000−2i−2i2i2i000000000002i−2i00002i−2i0000−2i−2i2i2i0000000000002i−2i00000000000-22000
χ4322-2-2222-222-2-2-22-2-22220-2-2-2222-2-2-2000000−2i2i2-2-220000000000002i2i−2i−2i00000000000−2i2i0000−2i2i00002i2i−2i−2i000000000000−2i2i00000000000-22000
χ4422-2-2222-222-2-2-22-2-22220-2-2-2222-2-2-2000000−2i2i2-2-22000000000000−2i−2i2i2i00000000000−2i2i0000−2i2i0000−2i−2i2i2i000000000000−2i2i000000000002-2000
χ452-22-22222-2-222-2-2-2-22220222-2-2-2-2-2-2002-22i−2i0022-2-20000000000002i−2i2i−2i0002-22-2002i−2i00002i−2i0000002i−2i2i−2i02-200000002i−2i000000000000000000
χ462-22-22222-2-222-2-2-2-22220222-2-2-2-2-2-2002-2−2i2i0022-2-2000000000000−2i2i−2i2i0002-22-200−2i2i0000−2i2i000000−2i2i−2i2i02-20000000−2i2i000000000000000000
χ472-22-22222-2-222-2-2-2-22220222-2-2-2-2-2-200-222i−2i0022-2-2000000000000−2i2i−2i2i000-22-22002i−2i00002i−2i000000−2i2i−2i2i0-2200000002i−2i000000000000000000
χ482-22-22222-2-222-2-2-2-22220222-2-2-2-2-2-200-22−2i2i0022-2-20000000000002i−2i2i−2i000-22-2200−2i2i0000−2i2i0000002i−2i2i−2i0-220000000−2i2i000000000000000000
χ492-22-22-1221-2-12-2-21-22-1-102-1-1-21111-23−32-22i−2i00-1-111003−3003−333−3−32i−2i2i−2i0002-2-11−i3i32i−2i003−3−ii000000−ii−ii0-11−i3i30003−3−ii000000000−i3i30000000
χ502-22-22-1221-2-12-2-21-22-1-102-1-1-21111-23−32-2−2i2i00-1-111003−3003−333−3−3−2i2i−2i2i0002-2-11i3−i3−2i2i003−3i−i000000i−ii−i0-11i3−i30003−3i−i000000000i3−i30000000
χ512-22-22-1221-2-12-2-21-22-1-102-1-1-21111-23−3-222i−2i00-1-111003−3003−333−3−3−2i2i−2i2i000-221-1−i3i32i−2i00−33−ii000000i−ii−i01-1−i3i3000−33−ii000000000i3−i30000000
χ522-22-22-1221-2-12-2-21-22-1-102-1-1-21111-23−3-22−2i2i00-1-111003−3003−333−3−32i−2i2i−2i000-221-1i3−i3−2i2i00−33i−i000000−ii−ii01-1i3−i3000−33i−i000000000−i3i30000000
χ532-22-22-1221-2-12-2-21-22-1-102-1-1-21111-2−332-22i−2i00-1-11100−3300−33−3−3332i−2i2i−2i0002-2-11i3−i32i−2i00−33−ii000000−ii−ii0-11i3−i3000−33−ii000000000i3−i30000000
χ542-22-22-1221-2-12-2-21-22-1-102-1-1-21111-2−332-2−2i2i00-1-11100−3300−33−3−333−2i2i−2i2i0002-2-11−i3i3−2i2i00−33i−i000000i−ii−i0-11−i3i3000−33i−i000000000−i3i30000000
χ552-22-22-1221-2-12-2-21-22-1-102-1-1-21111-2−33-222i−2i00-1-11100−3300−33−3−333−2i2i−2i2i000-221-1i3−i32i−2i003−3−ii000000i−ii−i01-1i3−i30003−3−ii000000000−i3i30000000
χ562-22-22-1221-2-12-2-21-22-1-102-1-1-21111-2−33-22−2i2i00-1-11100−3300−33−3−3332i−2i2i−2i000-221-1−i3i3−2i2i003−3i−i000000−ii−ii01-1−i3i30003−3i−i000000000i3−i30000000
χ572-2-22222-2-2-2-2-22-2222220-2-2-2-2-2-2222000000002-22-20000000000002-2-2200000000000000000002-22-22-2-2200000000000000000002-2002-200000
χ582-2-22222-2-2-2-2-22-2222220-2-2-2-2-2-2222000000002-22-20000000000002-2-220000000000000000000-22-222-2-220000000000000000000-2200-2200000
χ592-2-22222-2-2-2-2-22-2222220-2-2-2-2-2-2222000000002-22-2000000000000-222-200000000000000000002-2-22-222-200000000000000000002-200-2200000
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χ6144444-2-24-2-2-2-2-24-24-2-214-2-21-2-21-21-2-2-20044001111-24-2-2-2-211111100004000000-2-2-2-20000-2-20000000000-200110000011000000000000000000
χ6244444-2-24-2-2-2-2-24-24-2-214-2-21-2-21-21-2-2-200-4-4001111-24-2-2-2-21111110000-400000022220000220000000000200-1-100000-1-1000000000000000000
χ6344444-2-24-2-2-2-2-24-24-2-21-4-2-21-2-21-21-22200440011112-42222-1-1-1-1-1-10000-400000022-2-20000-2-20000000000200-1-10000011000000000000000000
χ6444444-2-24-2-2-2-2-24-24-2-21-4-2-21-2-21-21-22200-4-40011112-42222-1-1-1-1-1-100004000000-2-2220000220000000000-2001100000-1-1000000000000000000
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χ664444-24-2-24-24-2-2-24-21-2-241-2-21-2-2-2-21440000-4-41111-2-2-2-211-2-21111000000-4000000002200002200000000000002020000-1-1-1-100000000000000
χ674444-24-2-24-24-2-2-24-21-2-2-41-2-21-2-2-2-21-4-400004411112222-1-122-1-1-1-1000000-400000000-2-20000-2-20000000000000202000011-1-100000000000000
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χ704444-2-24-2-24-244-2-2-2-21-24-21-2-21-21-2-2-2-2-4-4000011114-211-2-2-2-2111100000-402222000000220000000000000-1-100020-1-100000000000000000000
χ714444-2-24-2-24-244-2-2-2-21-2-4-21-2-21-21-2-2224400001111-42-1-12222-1-1-1-100000-40-2-2-2-20000002200000000000001100020-1-100000000000000000000
χ724444-2-24-2-24-244-2-2-2-21-2-4-21-2-21-21-2-222-4-400001111-42-1-12222-1-1-1-100000402222000000-2-20000000000000-1-1000-201100000000000000000000
χ7344-4-444-2-44-2-4224-4-4-24-202-42-24-2-4220000004i−4i-222-2000000000000000000000000000−2i2i00004i−4i00000000000000000000−2i2i0000000000000000
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χ7744-4-4-244244-4-4-4-2-42-2-24022-4-2-242-420000004i−4i-222-20000000000000000000000000004i−4i0000−2i2i00000000000000000000−2i2i0000000000000000
χ7844-4-4-244244-4-4-4-2-42-2-24022-4-2-242-42000000−4i4i-222-2000000000000000000000000000−4i4i00002i−2i000000000000000000002i−2i0000000000000000
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χ8044-4-4-24-224-2-422-2-421-2-20-1221-2-222-10000004i−4i1-1-110000-3300-33-33000000000000000−2i2i0000−2i2i00000000000000000000i−i−3i3i00000000000000
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χ8244-4-4-24-224-2-422-2-421-2-20-1221-2-222-1000000−4i4i1-1-110000-3300-33-330000000000000002i−2i00002i−2i00000000000000000000−ii3i−3i00000000000000
χ834-44-444-24-424-22-4-4-4-24-20-24-22-42-42200004i−4i00-2-2220000000000000000000000000−2i2i00004i−4i00000000000000000000−2i2i000000000000000000
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χ854-44-44-2-2422-2-22-42-4-2-210-2-2122-12-1223−23004i−4i0011-1-10023−2300−33−3−33300000000000−2i32i3−2i2i0000−2i2i0000000000000i3−i300000i−i000000000000000000
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χ874-44-44-2-2422-2-22-42-4-2-210-2-2122-12-12−2323004i−4i0011-1-100−2323003−333−3−3000000000002i3−2i3−2i2i0000−2i2i0000000000000−i3i300000i−i000000000000000000
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χ894-44-4-244-2-4-444-42-42-2-240-2-2422-42-42004-40000-2-2220000000000000000000-224-4000000000000000000000-22000000000000000000000000000
χ904-44-4-244-2-4-444-42-42-2-240-2-2422-42-4200-440000-2-22200000000000000000002-2-440000000000000000000002-2000000000000000000000000000
χ914-44-4-2-24-22-4-24-4222-21-20-21-22-12-12223−234-4000011-1-100−330023−23−3−3330000000-22-2200000023−2300000000000001-100000−3300000000000000000000
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χ954-4-4444-2-4-42-42-2-444-24-202-422-424-2-200000000-22-22000000000000000000000000000000000004-40000000000000000000000000-22000000000
χ964-4-4444-2-4-42-42-2-444-24-202-422-424-2-200000000-22-2200000000000000000000000000000000000-4400000000000000000000000002-2000000000
χ974-4-444-24-42-42-44-4-244-2-20-422-422-2-2400000000-22-220000000000004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ984-4-444-24-42-42-44-4-244-2-20-422-422-2-2400000000-22-22000000000000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ994-4-44-2442-4-4-4-4424-2-2-24022-422-4-24-200000000-22-2200000000000000000000000000000000000004-4000000000000000000000000000-2200000
χ1004-4-44-2442-4-4-4-4424-2-2-24022-422-4-24-200000000-22-220000000000000000000000000000000000000-440000000000000000000000000002-200000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-4-8-4-444484-8-4-42044-2-4-424-24000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-484-484-8-8-444-42-404-24-42-4-244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-44-4-4444-4442220-2-2-2222-2-2-200000000-111-100006-600-33-330000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4-4444-4442220-2-2-2222-2-2-200000000-111-10000-66003-33-30000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-4-4-848-444-842-4-402-4-4-24444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-444-4-444442220222-2-2-2-2-2-243−43000000-1-11100−232300−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-444-4-444442220222-2-2-2-2-2-2−4343000000-1-1110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-4-84444-4-8-48-4-42044-244-2-42-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-44-84-84-448-42-4-40-244-244-4-42000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4844-84-884-4-4-42-404-244-242-4-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444444-44-4-42220-2-2-2-2-2-222200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444444-44-4-42220-2-2-2-2-2-222200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000000

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