Finite Group Databasebeta

← Group #13169326

Character table — Group #13169326

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212444121212121212121212121212121212124444121212121212121212121212121212121212121244441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-111111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111111-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-11111-1-111-1-111111-11-111-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-11-11-1-111-1-111-111
χ51111111111111111111111111111111-1-1111111111111111111111-11-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-1111111-11-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11-11-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-11111-1-1111111-11-1-111-1-1-1-11111-1-1-111-111-1-1-1-111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111111-1-1-1-111-1-1111-1-11-1-111-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1111111-1-11111111-1-1-1-1-11111-1-111-1-11-1-11-1-111-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-11111111-111-1-11111-1-1-1-111-111-111-1-1-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111111111-1-1-1
χ17222222-122-1-12222-12-1-122-1-12-1-1-1-12-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-10222222-1-1-1-1-1-1-1-100002222-1-1-1-12200-1-1-1-1-1-1-1-1000000000000-1-100000
χ18222222-122-1-12222-12-1-122-1-12-1-1-1-12-1-122-2-200-1-1-1-12222-1-1-1-1-1-1-1-102-222-2-2-1-111-1-1110000-2-2-2-211112-200-1-111-1-1110000000000001100000
χ19222222-122-1-12222-12-1-122-1-12-1-1-1-12-1-1-2-22200-1-1-1-12222-1-1-1-1-1-1-1-10-22-2-22211-1-111-1-10000-2-2-2-21111-220011-1-111-1-10000000000001100000
χ20222222-122-1-12222-12-1-122-1-12-1-1-1-12-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-2-2-21111111100002222-1-1-1-1-2-20011111111000000000000-1-100000
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χ22222222-122-1-12222-12-1-1-22-1-12-1-1-1-121122-2-200-1-1-1-1-2-2-2-2111111110-2222-2-211-1-1-1-1110000-2-222-1-1-1-1-2200-1-11111-1-10000000000001100000
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χ2522222-122-1222-12-12-12-12-12-1-12-12-1-122002222-1-1-1-12-1-1-122-1-1-1-1-1-120200-1-10022002222-1-1000000000-12-100-1-100-1-1-1-1-1-1020200-1-100000-10
χ2622222-122-1222-12-12-12-12-12-1-12-12-1-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20200-1-100220022-2-211000000000-1-2100-1-100-1-111110-20-200110000010
χ2722222-122-1222-12-12-12-12-12-1-12-12-1-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-120-2001100-2-200-2-222-1-100000000012-100110011-1-1-1-10-20-200110000010
χ2822222-122-1222-12-12-12-12-12-1-12-12-1-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-2001100-2-200-2-2-2-2110000000001-21001100111111020200-1-100000-10
χ2922222-122-1222-12-12-12-1-2-12-1-12-12-1-1-2-2002222-1-1-1-1-2111-2-2111111-20-200-1-100-2-2002222-1-10000000001-2100-1-10011-1-1110-20200-1-10000010
χ3022222-122-1222-12-12-12-1-2-12-1-12-12-1-1-2-20022-2-2-1-1-1-1-2111-2-211111120-200-1-100-2-20022-2-21100000000012-100-1-1001111-1-1020-2001100000-10
χ3122222-122-1222-12-12-12-1-2-12-1-12-12-1-1-2-200-2-222-1-1-1-1-2111-2-2111111-2020011002200-2-222-1-1000000000-1-21001100-1-1-1-111020-2001100000-10
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χ372222-122-1222-12-122-1-12-2-1-12-1-12-12-1-2-2220022-1-1-1-11-21111-2-21111-2-20-1-100-2-2002200-1-12200000000101-2-1-1001100-1-111-2020-1-1000000100
χ382222-122-1222-12-122-1-12-2-1-12-1-12-12-1-2-22200-2-2-1-1-1-11-21111-2-211112-20-1-100-2-200220011-2-20000000010-12-1-100110011-1-120-2011000000-100
χ392222-122-1222-12-122-1-12-2-1-12-1-12-12-1-2-2-2-20022-1-1-1-11-21111-2-21111-22011002200-2-200-1-12200000000-101-21100-1-100-1-11120-2011000000-100
χ402222-122-1222-12-122-1-12-2-1-12-1-12-12-1-2-2-2-200-2-2-1-1-1-11-21111-2-2111122011002200-2-20011-2-200000000-10-121100-1-10011-1-1-2020-1-1000000100
χ4122-2-222222-2-2-2-2-2-2222202-2-2-222-2-2-2002-22-20022-2-20000000000000002-22-200002-22-200002-200000000002-22-200000000000000002-200000
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χ4722-2-222-12211-2-2-2-2-12-1-10211-2-1-111-23−3-222-200-1-11100003−33−333−3−3000-222-2−333−31-1-110000-2200−3−33300001-1-11−333−30000000000001-100000
χ4822-2-222-12211-2-2-2-2-12-1-10211-2-1-111-23−3-22-2200-1-11100003−33−333−3−3000-22-22−33−331-11-100002-20033−3−300001-11-1−33−33000000000000-1100000
χ4922-2-222-12211-2-2-2-2-12-1-10211-2-1-111-2−332-22-200-1-1110000−33−33−3−3330002-22-2−33−33-11-1100002-200−3−3330000-11-11−33−33000000000000-1100000
χ5022-2-222-12211-2-2-2-2-12-1-10211-2-1-111-2−332-2-2200-1-1110000−33−33−3−3330002-2-22−333−3-111-10000-220033−3−30000-111-1−333−30000000000001-100000
χ5122-2-222-12211-2-2-2-2-12-1-10211-2-1-111-2−33-222-200-1-1110000−33−33−3−333000-222-23−3−331-1-110000-220033−3−300001-1-113−3−330000000000001-100000
χ5222-2-222-12211-2-2-2-2-12-1-10211-2-1-111-2−33-22-2200-1-1110000−33−33−3−333000-22-223−33−31-11-100002-200−3−33300001-11-13−33−3000000000000-1100000
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χ934-4-44-2442-44-4-242-4-4-2-24022-4-22-4-242000000−4i4i-222-20000000000000000000000000002i−2i−4i4i000000000000000000002i−2i00000000000000000
χ944-4-44-2-24224-4-2-222-41-2-20-122122-2-2-10000004i−4i1-1-11003-300003-33-3000000000000000−2i2i−2i2i00000000000000000000i−i3i−3i000000000000000
χ954-4-44-2-24224-4-2-222-41-2-20-122122-2-2-10000004i−4i1-1-1100-330000-33-33000000000000000−2i2i−2i2i00000000000000000000i−i−3i3i000000000000000
χ964-4-44-2-24224-4-2-222-41-2-20-122122-2-2-1000000−4i4i1-1-11003-300003-33-30000000000000002i−2i2i−2i00000000000000000000−ii−3i3i000000000000000
χ974-4-44-2-24224-4-2-222-41-2-20-122122-2-2-1000000−4i4i1-1-1100-330000-33-330000000000000002i−2i2i−2i00000000000000000000−ii3i−3i000000000000000
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
χ10088-8-8-4-48-4-4-8-8444482-4-40244-2-4-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-4444444-422202-2-2-222-2-2-243−43000000-1-1110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4444444-422202-2-2-222-2-2-2−4343000000-1-111000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-844-4-848-44-4-4204-4244-24-2-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-44-84-44-8-484-42-4042-44-24-24-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4844-8844-4-4-82-4-40-2-4-4-244442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444-444-4-442220-222-2-2-2-2-2200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4444-444-4-442220-222-2-2-2-2-2200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4-84-448-4-844-4-42044-2-44-2-424000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-44-8-44-484-84-42-404-24-4-242-44000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-44-4-44442220-2-2-22-2-222-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-44-4-44442220-2-2-22-2-222-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000

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