Finite Group Databasebeta

← Group #13169322

Character table — Group #13169322

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212444121212121212121212121212121212124444121212121212121212121212121212121212121244441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-1-1-111111111111111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-11111-1-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111111111-1-1-1-1111111-11-1-111-1-1-1-1-1-111111-1-11-1-111-1-111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111-111111-1-111-1-111-1-1-111-1-1-1-1-111-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-1-111-1-11111111-1-1-1-1-111-1-111-1-111-111-1-1-1-1-111111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-111-1-11111111-111-1-1111111-1-1-1-11-1-11-1-111-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-111111111-1-1-1
χ17222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-12202222-1-1-1-10000-1-1-1-12222-1-1-1-12200-1-1-1-100-1-1-1-1000000-1-1000000000
χ18222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-122-2-200-1-1-1-12222-1-1-1-1-1-1-1-12-2022-2-2-1-1110000-1-111-2-2-2-211112-200-1-11100-1-11100000011000000000
χ19222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-1-2-22200-1-1-1-12222-1-1-1-1-1-1-1-1-220-2-22211-1-1000011-1-1-2-2-2-21111-220011-1-10011-1-100000011000000000
χ20222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-2-20-2-2-2-21111000011112222-1-1-1-1-2-2001111001111000000-1-1000000000
χ21222222-12222-1-1-1222-1-1-22-1-12-1-12-1-111222200-1-1-1-1-2-2-2-211111111-2-20222211110000-1-1-1-122-2-21111-2-200-1-1-1-1001111000000-1-1000000000
χ22222222-12222-1-1-1222-1-1-22-1-12-1-12-1-11122-2-200-1-1-1-1-2-2-2-211111111-22022-2-211-1-10000-1-111-2-222-1-1-1-1-2200-1-1110011-1-100000011000000000
χ23222222-12222-1-1-1222-1-1-22-1-12-1-12-1-111-2-22200-1-1-1-1-2-2-2-2111111112-20-2-222-1-111000011-1-1-2-222-1-1-1-12-20011-1-100-1-11100000011000000000
χ24222222-12222-1-1-1222-1-1-22-1-12-1-12-1-111-2-2-2-200-1-1-1-1-2-2-2-211111111220-2-2-2-2-1-1-1-10000111122-2-211112200111100-1-1-1-1000000-1-1000000000
χ2522222-122-12-12222-1-12-12-12-1-12-1-12-122002222-1-1-1-12-1-1-122-1-1-1-1-1-102200-1-1002222-1-10022000000000-12-100-1-1-1-100-1-1-1-100220000-1-1000-10
χ2622222-122-12-12222-1-12-12-12-1-12-1-12-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-102-200-1-10022-2-2110022000000000-1-2100-1-11100-1-11100-2-200001100010
χ2722222-122-12-12222-1-12-12-12-1-12-1-12-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-10-22001100-2-222-1-100-2-200000000012-10011-1-10011-1-100-2-200001100010
χ2822222-122-12-12222-1-12-12-12-1-12-1-12-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2001100-2-2-2-21100-2-20000000001-2100111100111100220000-1-1000-10
χ2922222-122-12-12222-1-12-1-2-12-1-12-1-12-1-2-2002222-1-1-1-1-2111-2-21111110-2-200-1-100-2-222-1-100220000000001-2100-1-1110011-1-1002-20000-1-100010
χ3022222-122-12-12222-1-12-1-2-12-1-12-1-12-1-2-20022-2-2-1-1-1-1-2111-2-21111110-2200-1-100-2-2-2-211002200000000012-100-1-1-1-100111100-22000011000-10
χ3122222-122-12-12222-1-12-1-2-12-1-12-1-12-1-2-200-2-222-1-1-1-1-2111-2-211111102-20011002222-1-100-2-2000000000-1-2100111100-1-1-1-100-22000011000-10
χ3222222-122-12-12222-1-12-1-2-12-1-12-1-12-1-2-200-2-2-2-2-1-1-1-1-2111-2-211111102200110022-2-21100-2-2000000000-12-10011-1-100-1-111002-20000-1-100010
χ332222-122-12-12222-12-1-122-1-12-1-12-1-1222220022-1-1-1-1-12-1-1-1-122-1-1-1-1202-1-1002200-1-122220000000000-10-12-1-100-1-1-1-100-1-1220000-1-10000-100
χ342222-122-12-12222-12-1-122-1-12-1-12-1-12222200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-120-2-1-100220011-2-2220000000000-101-2-1-10011-1-10011-2-20000110000100
χ352222-122-12-12222-12-1-122-1-12-1-12-1-1222-2-20022-1-1-1-1-12-1-1-1-122-1-1-1-1-2021100-2-200-1-122-2-2000000000010-121100-1-11100-1-1-2-20000110000100
χ362222-122-12-12222-12-1-122-1-12-1-12-1-1222-2-200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-21100-2-20011-2-2-2-20000000000101-2110011110011220000-1-10000-100
χ372222-122-12-12222-12-1-12-2-1-12-1-12-1-12-2-2220022-1-1-1-11-21111-2-21111-20-2-1-100-2-200-1-122220000000000101-2-1-100111100-1-12-20000-1-10000100
χ382222-122-12-12222-12-1-12-2-1-12-1-12-1-12-2-22200-2-2-1-1-1-11-21111-2-21111-202-1-100-2-20011-2-222000000000010-12-1-100-1-1110011-220000110000-100
χ392222-122-12-12222-12-1-12-2-1-12-1-12-1-12-2-2-2-20022-1-1-1-11-21111-2-2111120-211002200-1-122-2-20000000000-101-2110011-1-100-1-1-220000110000-100
χ402222-122-12-12222-12-1-12-2-1-12-1-12-1-12-2-2-2-200-2-2-1-1-1-11-21111-2-211112021100220011-2-2-2-20000000000-10-121100-1-1-1-100112-20000-1-10000100
χ4122-2-222222-2-2-2-22-2-222202-2-2-222-2-2-2002-22-20022-2-20000000000000002-22-2000000002-22-22-200000000002-22-20000000000002-2000000000
χ4222-2-222222-2-2-2-22-2-222202-2-2-222-2-2-2002-2-220022-2-20000000000000002-2-22000000002-2-22-2200000000002-2-22000000000000-22000000000
χ4322-2-222222-2-2-2-22-2-222202-2-2-222-2-2-200-222-20022-2-2000000000000000-222-200000000-222-2-220000000000-222-2000000000000-22000000000
χ4422-2-222222-2-2-2-22-2-222202-2-2-222-2-2-200-22-220022-2-2000000000000000-22-2200000000-22-222-20000000000-22-220000000000002-2000000000
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χ4622-2-222-122-2-211-1-2-22-1-10211-2-1-1-2113−32-2-2200-1-11100003−33−333−3−30002-2-223−3−330000-111-1-2200−3−3330000-111-1003−3−330000001-1000000000
χ4722-2-222-122-2-211-1-2-22-1-10211-2-1-1-2113−3-222-200-1-11100003−33−333−3−3000-222-2−333−300001-1-11-2200−3−33300001-1-1100−333−30000001-1000000000
χ4822-2-222-122-2-211-1-2-22-1-10211-2-1-1-2113−3-22-2200-1-11100003−33−333−3−3000-22-22−33−3300001-11-12-20033−3−300001-11-100−33−33000000-11000000000
χ4922-2-222-122-2-211-1-2-22-1-10211-2-1-1-211−332-22-200-1-1110000−33−33−3−3330002-22-2−33−330000-11-112-200−3−3330000-11-1100−33−33000000-11000000000
χ5022-2-222-122-2-211-1-2-22-1-10211-2-1-1-211−332-2-2200-1-1110000−33−33−3−3330002-2-22−333−30000-111-1-220033−3−30000-111-100−333−30000001-1000000000
χ5122-2-222-122-2-211-1-2-22-1-10211-2-1-1-211−33-222-200-1-1110000−33−33−3−333000-222-23−3−3300001-1-11-220033−3−300001-1-11003−3−330000001-1000000000
χ5222-2-222-122-2-211-1-2-22-1-10211-2-1-1-211−33-22-2200-1-1110000−33−33−3−333000-22-223−33−300001-11-12-200−3−33300001-11-1003−33−3000000-11000000000
χ532-2-22222-2-2-2-2-22-2222220-2222-2-2-2-2-20000002i−2i2-22-2000000000000000000000002i−2i2i−2i0000002-22-22-2000000000000002i−2i00000000002i−2i000
χ542-2-22222-2-2-2-2-22-2222220-2222-2-2-2-2-20000002i−2i2-22-2000000000000000000000002i−2i2i−2i000000-22-22-22000000000000002i−2i0000000000−2i2i000
χ552-2-22222-2-2-2-2-22-2222220-2222-2-2-2-2-2000000−2i2i2-22-200000000000000000000000−2i2i−2i2i0000002-22-22-200000000000000−2i2i0000000000−2i2i000
χ562-2-22222-2-2-2-2-22-2222220-2222-2-2-2-2-2000000−2i2i2-22-200000000000000000000000−2i2i−2i2i000000-22-22-2200000000000000−2i2i00000000002i−2i000
χ5744444-2-24-24-2-2-2-24-2-2-214-2-21-2-21-2-21-2-200440011114-2-2-2-2-211111104000-2-200-2-2000000-2-2000000000-200001100001100000000000000000
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χ6044444-2-24-24-2-2-2-24-2-2-21-4-2-21-2-21-2-212200-4-4001111-422222-1-1-1-1-1-1040002200-2-200000022000000000-20000-1-100001100000000000000000
χ614444-24-2-24-24-2-2-2-24-21-24-21-2-21-2-21-2-2-24400001111-24-2-211-2-21111400-2-200-2-2000000-2-20000000000-2000110000110000000000000000000
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χ934-4-44-2442-42-4-44-4-24-2-2402-24-22-422-4000000−4i4i-22-22000000000000000000000002i−2i−4i4i000000000000000000000000002i−2i000000000000000
χ944-4-44-2-242222-44-4-2-21-2-20-1-2-2122-1220000004i−4i1-11-1003i−3i00003i−3i3i−3i00000000000−2i2i−2i2i000000000000000000003-30000i−i000000000000000
χ954-4-44-2-242222-44-4-2-21-2-20-1-2-2122-1220000004i−4i1-11-100−3i3i0000−3i3i−3i3i00000000000−2i2i−2i2i00000000000000000000-330000i−i000000000000000
χ964-4-44-2-242222-44-4-2-21-2-20-1-2-2122-122000000−4i4i1-11-1003i−3i00003i−3i3i−3i000000000002i−2i2i−2i00000000000000000000-330000−ii000000000000000
χ974-4-44-2-242222-44-4-2-21-2-20-1-2-2122-122000000−4i4i1-11-100−3i3i0000−3i3i−3i3i000000000002i−2i2i−2i000000000000000000003-30000−ii000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-48-4-444-8-88442-4-40244-2-4-4-2440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-44444-44422202-2-2-222-2-2-243−43000000-1-1110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-44444-44422202-2-2-222-2-2-2−4343000000-1-111000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-848-4-444-84-4-42044-244-2-4-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-44-8-48-4444-8-42-404-244-24-42-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4844-4-48-8-8442-4-40-244-2442-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-4-4-444442220-2-2-2-2-2-222200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-4-4-444442220-2-2-2-2-2-222200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4-84-844-448-4-4-4204-42-44-244-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-44-84-84-44-48-42-4042-4-4-244-24000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444444-44-4-42220-2222-2-2-2-2-200000000-11-11006i−6i0000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444444-44-4-42220-2222-2-2-2-2-200000000-11-1100−6i6i00003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000

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