Finite Group Databasebeta

← Group #13168301

Character table — Group #13168301

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212244466666612121212121212121212441212121266666121212121212121212121244444121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1111111-1-1111111-1-111111111111-1-111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-11111111-1-111-1-111-1-111-1-1-1-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-11-111
χ51111111111111111111111111111111-1-111111111111111111111-11-1-1-1-1111111-1-11111-1-1-1-1-1-11-1-11111-1-1-1111111-1-1-111-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-11111-1-11-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-111-1-1111111-111-1-11-1-1-1-111-1-1111-1-11-1-1-111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-11111111111-111-1-1-11-1-1-11111-1-1-11-1-11-1-1-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-11-1111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-11-1-1-1-1-111-1-1-1111-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111-1111-1111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11-1111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-11111111-1-1111-1111-1-1-1-111-11-1-11-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-111-1-1111111111-1-111-11111-1-111-1-11-1-11-1-1-111-1-1-11-11
χ17222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-12222-1-1-1-122-1-1-1-122-1-1-1-1202022-1-1-1-10022-1-1-1-10022-1-1-1-12-1-1-1-1002-1-1-1-1000000200-1-100000000
χ18222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-1-202022-1-11100-2-2-1-11100-2-21111-2-1-111002-1-111000000-2001100000000
χ19222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-120-20-2-211-1-1002211-1-100-2-21111211-1-100-211-1-1000000-2001100000000
χ20222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-20-20-2-2111100-2-211110022-1-1-1-1-2111100-21111000000200-1-100000000
χ21222222-12-1222-1-1222-1-1-22-1-1-1-12-1-12112222-1-1-1-1-2-21111-2-21111-20-2022-1-111002211-1-10022-1-1-1-1-2-1-11100-211-1-1000000-2001100000000
χ22222222-12-1222-1-1222-1-1-22-1-1-1-12-1-121122-2-2-1-1-1-1-2-21111-2-2111120-2022-1-1-1-100-2-2111100-2-211112-1-1-1-100-21111000000200-1-100000000
χ23222222-12-1222-1-1222-1-1-22-1-1-1-12-1-1211-2-222-1-1-1-1-2-21111-2-21111-2020-2-211110022-1-1-1-100-2-21111-21111002-1-1-1-1000000200-1-100000000
χ24222222-12-1222-1-1222-1-1-22-1-1-1-12-1-1211-2-2-2-2-1-1-1-1-2-21111-2-211112020-2-211-1-100-2-2-1-1110022-1-1-1-1211-1-1002-1-111000000-2001100000000
χ2522222-12222-1-122-12-12-12-12-12-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12202000022-1-1-1-1002222000000-100-1-12-1000-1-1-1-1-1-10002200-1-100-1000
χ2622222-12222-1-122-12-12-12-12-12-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12-20-200002211-1-10022-2-2000000-100-1-1-21000-1-11111000-2-20011001000
χ2722222-12222-1-122-12-12-12-12-12-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-22020000-2-2-1-11100-2-222000000100112-100011-1-1-1-1000-2-20011001000
χ2822222-12222-1-122-12-12-12-12-12-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-20000-2-2111100-2-2-2-200000010011-210001111110002200-1-100-1000
χ2922222-12222-1-122-12-12-1-2-12-12-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-220-20000-2-2-1-1-1-10022-2-20000001001121000-1-111-1-10002-200-1-1001000
χ3022222-12222-1-122-12-12-1-2-12-12-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-2-2020000-2-211-1-100222200000010011-2-1000-1-1-1-111000-22001100-1000
χ3122222-12222-1-122-12-12-1-2-12-12-1-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111220-2000022-1-11100-2-2-2-2000000-100-1-1210001111-1-1000-22001100-1000
χ3222222-12222-1-122-12-12-1-2-12-12-1-12-1-1-2-200-2-2-1-1-1-1-21-2-2111111112-202000022111100-2-222000000-100-1-1-2-100011-1-1110002-200-1-1001000
χ332222-122-12-122222-1-1-122-1-12-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-10222-1-1220022002200-1-10000000-1-100-12-1-1-100-1-1-1-1220000000-1-10-100
χ342222-122-12-122222-1-1-122-1-12-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-10-22-2-1-12200-2-2002200110000000-1-1001-2-1-1-1001111-2-20000000110100
χ352222-122-12-122222-1-1-122-1-12-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-102-2211-2-2002200-2-200-1-100000001100-1211100-1-1-1-1-2-20000000110100
χ362222-122-12-122222-1-1-122-1-12-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-211-2-200-2-200-2-20011000000011001-2111001111220000000-1-10-100
χ372222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-11-211-2-211111102-2-2-1-122002200-2-200110000000-1-100-1-21110011-1-12-20000000110-100
χ382222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-11-211-2-21111110-2-22-1-12200-2-200-2-200-1-10000000-1-1001211100-1-111-220000000-1-10100
χ392222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111022-211-2-200220022001100000001100-1-2-1-1-10011-1-1-220000000-1-10100
χ402222-122-12-122222-1-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-11-211-2-21111110-22211-2-200-2-2002200-1-10000000110012-1-1-100-1-1112-20000000110-100
χ412-2-222222-2-2-2-22-22-22220222-2-2-2-2-2-2002-22i−2i22-2-200000000000000002-22-200002i−2i002i−2i002i−2i2i2i−2i−2i02-200000002i−2i0000000000000000000
χ422-2-222222-2-2-2-22-22-22220222-2-2-2-2-2-2002-2−2i2i22-2-200000000000000002-22-20000−2i2i00−2i2i00−2i2i−2i−2i2i2i02-20000000−2i2i0000000000000000000
χ432-2-222222-2-2-2-22-22-22220222-2-2-2-2-2-200-222i−2i22-2-20000000000000000-22-2200002i−2i002i−2i00−2i2i−2i−2i2i2i0-2200000002i−2i0000000000000000000
χ442-2-222222-2-2-2-22-22-22220222-2-2-2-2-2-200-22−2i2i22-2-20000000000000000-22-220000−2i2i00−2i2i002i−2i2i2i−2i−2i0-220000000−2i2i0000000000000000000
χ452-2-2222-121-2-2-2-112-22-1-102-1-111-211-23−32-22i−2i-1-111003−33−30033−3−300002-2-11−i3i3002i−2i3−3−ii002i−2i−i−iii0-11−i3i30003−3−ii000000000−i3i300000000
χ462-2-2222-121-2-2-2-112-22-1-102-1-111-211-23−32-2−2i2i-1-111003−33−30033−3−300002-2-11i3−i300−2i2i3−3i−i00−2i2iii−i−i0-11i3−i30003−3i−i000000000i3−i300000000
χ472-2-2222-121-2-2-2-112-22-1-102-1-111-211-23−3-222i−2i-1-111003−33−30033−3−30000-221-1−i3i3002i−2i−33−ii00−2i2iii−i−i01-1−i3i3000−33−ii000000000i3−i300000000
χ482-2-2222-121-2-2-2-112-22-1-102-1-111-211-23−3-22−2i2i-1-111003−33−30033−3−30000-221-1i3−i300−2i2i−33i−i002i−2i−i−iii01-1i3−i3000−33i−i000000000−i3i300000000
χ492-2-2222-121-2-2-2-112-22-1-102-1-111-211-2−332-22i−2i-1-11100−33−3300−3−33300002-2-11i3−i3002i−2i−33−ii002i−2i−i−iii0-11i3−i3000−33−ii000000000i3−i300000000
χ502-2-2222-121-2-2-2-112-22-1-102-1-111-211-2−332-2−2i2i-1-11100−33−3300−3−33300002-2-11−i3i300−2i2i−33i−i00−2i2iii−i−i0-11−i3i3000−33i−i000000000−i3i300000000
χ512-2-2222-121-2-2-2-112-22-1-102-1-111-211-2−33-222i−2i-1-11100−33−3300−3−3330000-221-1i3−i3002i−2i3−3−ii00−2i2iii−i−i01-1i3−i30003−3−ii000000000−i3i300000000
χ522-2-2222-121-2-2-2-112-22-1-102-1-111-211-2−33-22−2i2i-1-11100−33−3300−3−3330000-221-1−i3i300−2i2i3−3i−i002i−2i−i−iii01-1−i3i30003−3i−i000000000i3−i300000000
χ5344444-2-24-24-2-2-2-2-24-2-214-2-21-21-2-21-2-2-2004411114-2-2-211-2-2111140000000-2-200-2-200-2-200000000-2001100000110000000000000000000
χ5444444-2-24-24-2-2-2-2-24-2-214-2-21-21-2-21-2-2-200-4-411114-2-2-211-2-21111-40000000220022002200000000200-1-100000-1-10000000000000000000
χ5544444-2-24-24-2-2-2-2-24-2-21-4-2-21-21-2-21-22200441111-4222-1-122-1-1-1-1-400000002200-2-200-2-200000000200-1-100000110000000000000000000
χ5644444-2-24-24-2-2-2-2-24-2-21-4-2-21-21-2-21-22200-4-41111-4222-1-122-1-1-1-140000000-2-20022002200000000-2001100000-1-10000000000000000000
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χ594444-24-2-2-2-244-2-24-2-21-2-4-21-21-2-21-2-222440011112-4-1-12222-1-1-1-100-40-2-2-2-200000022000000000001100002-1-1000000000000000000000
χ604444-24-2-2-2-244-2-24-2-21-2-4-21-21-2-21-2-222-4-40011112-4-1-12222-1-1-1-100402222000000-2-200000000000-1-10000-211000000000000000000000
χ614444-2-24-24-2-2-244-2-21-2-241-2-2-2-21-2-214400001111-2-2-2-2-2-21111110404000000-2-2000000-2-200000000000-2-2000001111000000000000000
χ624444-2-24-24-2-2-244-2-21-2-241-2-2-2-21-2-214400001111-2-2-2-2-2-21111110-40-40000002200000022000000000002200000-1-1-1-1000000000000000
χ634444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-21-2-21-4-400001111222222-1-1-1-1-1-1040-4000000-2-20000002200000000000-2200000-1-111000000000000000
χ644444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-21-2-21-4-400001111222222-1-1-1-1-1-10-40400000022000000-2-2000000000002-20000011-1-1000000000000000
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χ874-4-444-2-242-422-22-2-4-2-210-2-212-122-12−2323004i−4i11-1-100−23233−30033−3−3000000002i3−2i300−2i2i00−2i2i00000000000−i3i300000i−i0000000000000000000
χ884-4-444-2-242-422-22-2-4-2-210-2-212-122-12−232300−4i4i11-1-100−23233−30033−3−300000000−2i32i3002i−2i002i−2i00000000000i3−i300000−ii0000000000000000000
χ894-4-44-244-2-42-4-44-442-2-240-2-242-422-42004-400-2-2220000000000000000-224-40000000000000000000-220000000000000000000000000000
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χ924-4-44-24-2-222-4-4-2242-21-20-21-2-122-12223−23-440011-1-100−3323−2300−3−33300002-22-2000000−232300000000000-11000003−3000000000000000000000
χ934-4-44-24-2-222-4-4-2242-21-20-21-2-122-122−23234-40011-1-1003−3−23230033−3−30000-22-22000000−2323000000000001-1000003−3000000000000000000000
χ944-4-44-24-2-222-4-4-2242-21-20-21-2-122-122−2323-440011-1-1003−3−23230033−3−300002-22-200000023−2300000000000-1100000−33000000000000000000000
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
χ9788-8-88-4-4-8-48-44444-8-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-44-4-48-844-84-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4848-4-44-8-8442-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-44-4-4-4444442220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-4-4-4444442220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-4-84-84-44-448-4-42044-24-2-4-4240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4444-884-4-8-4-42-404-24-24-42-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44444-44-44-42220-2-2-2-2-2222-2000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44444-44-44-42220-2-2-2-2-2222-2000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-4-84448-8-442-4-402-4-444-244-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-44444-44-442220222-2-2-2-2-2-243−430000-1-11100−2323−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-44444-44-442220222-2-2-2-2-2-2−43430000-1-1110023−2323−2300−3−333000000000000000000000000000000000000000000000000000000000

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