Finite Group Databasebeta

← Group #13169321

Character table — Group #13169321

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212444121212121212121212121212121212124444121212121212121212121212121212121212121244441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-1111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-11111-1-111-1-111111-11-111-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-11-11-1-111-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-1111111-11-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11-11-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11
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
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-11111-1-1111111-11-1-111-1-1-1-11111-1-1-111-111-1-1-1-111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111111-1-1-1-111-1-1111-1-11-1-111-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-11111111-1-1-1-1-11111-1-111-1-11-1-11-1-111-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111-1-1-1-1-1-11111111-111-1-11111-1-1-1-111-111-111-1-1-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1111
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
χ17222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-1222200-1-1-1-122-1-1-1-122-1-1-1-12202222-1-1-1-1-1-1-1-100002222-1-1-1-12200-1-1-1-1-1-1-1-1000000000000-1-100000
χ18222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-12-2022-2-2-1-111-1-1110000-2-2-2-211112-200-1-111-1-1110000000000001100000
χ19222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-1-220-2-22211-1-111-1-10000-2-2-2-21111-220011-1-111-1-10000000000001100000
χ20222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-20-2-2-2-21111111100002222-1-1-1-1-2-20011111111000000000000-1-100000
χ21222222-122-122-1-1222-1-1-222-1-1-1-1-1-1211222200-1-1-1-1-2-21111-2-21111-2-2022221111-1-1-1-1000022-2-21111-2-200-1-1-1-11111000000000000-1-100000
χ22222222-122-122-1-1222-1-1-222-1-1-1-1-1-121122-2-200-1-1-1-1-2-21111-2-21111-22022-2-211-1-1-1-1110000-2-222-1-1-1-1-2200-1-11111-1-10000000000001100000
χ23222222-122-122-1-1222-1-1-222-1-1-1-1-1-1211-2-22200-1-1-1-1-2-21111-2-211112-20-2-222-1-11111-1-10000-2-222-1-1-1-12-20011-1-1-1-1110000000000001100000
χ24222222-122-122-1-1222-1-1-222-1-1-1-1-1-1211-2-2-2-200-1-1-1-1-2-21111-2-21111220-2-2-2-2-1-1-1-11111000022-2-2111122001111-1-1-1-1000000000000-1-100000
χ2522222-122-122-1222-1-12-12-1-12-12-12-1-122002222-1-1-1-12-122-1-1-1-1-1-1-1-102200-1-10022002222-1-1000000000-12-100-1-100-1-1-1-1-1-1020200-1-100000-10
χ2622222-122-122-1222-1-12-12-1-12-12-12-1-1220022-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-200-1-100220022-2-211000000000-1-2100-1-100-1-111110-20-200110000010
χ2722222-122-122-1222-1-12-12-1-12-12-12-1-12200-2-222-1-1-1-12-122-1-1-1-1-1-1-1-10-22001100-2-200-2-222-1-100000000012-100110011-1-1-1-10-20-200110000010
χ2822222-122-122-1222-1-12-12-1-12-12-12-1-12200-2-2-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2001100-2-200-2-2-2-2110000000001-21001100111111020200-1-100000-10
χ2922222-122-122-1222-1-12-1-2-1-12-12-12-1-1-2-2002222-1-1-1-1-21-2-2111111110-2-200-1-100-2-2002222-1-10000000001-2100-1-10011-1-1110-20200-1-10000010
χ3022222-122-122-1222-1-12-1-2-1-12-12-12-1-1-2-20022-2-2-1-1-1-1-21-2-2111111110-2200-1-100-2-20022-2-21100000000012-100-1-1001111-1-1020-2001100000-10
χ3122222-122-122-1222-1-12-1-2-1-12-12-12-1-1-2-200-2-222-1-1-1-1-21-2-21111111102-20011002200-2-222-1-1000000000-1-21001100-1-1-1-111020-2001100000-10
χ3222222-122-122-1222-1-12-1-2-1-12-12-12-1-1-2-200-2-2-2-2-1-1-1-1-21-2-2111111110220011002200-2-2-2-211000000000-12-1001100-1-111-1-10-20200-1-10000010
χ332222-122-122-1222-12-1-122-1-1-12-12-12-122220022-1-1-1-1-12-1-122-1-1-1-1-1-1202-1-10022002200-1-12200000000-10-12-1-100-1-100-1-1-1-12020-1-1000000-100
χ342222-122-122-1222-12-1-122-1-1-12-12-12-1222200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-120-2-1-1002200220011-2-200000000-101-2-1-100-1-1001111-20-2011000000100
χ352222-122-122-1222-12-1-122-1-1-12-12-12-122-2-20022-1-1-1-1-12-1-122-1-1-1-1-1-1-2021100-2-200-2-200-1-1220000000010-1211001100-1-1-1-1-20-2011000000100
χ362222-122-122-1222-12-1-122-1-1-12-12-12-122-2-200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-20-21100-2-200-2-20011-2-200000000101-21100110011112020-1-1000000-100
χ372222-122-122-1222-12-1-12-2-1-1-12-12-12-1-2-2220022-1-1-1-11-211-2-2111111-20-2-1-100-2-2002200-1-12200000000101-2-1-1001100-1-111-2020-1-1000000100
χ382222-122-122-1222-12-1-12-2-1-1-12-12-12-1-2-22200-2-2-1-1-1-11-211-2-2111111-202-1-100-2-200220011-2-20000000010-12-1-100110011-1-120-2011000000-100
χ392222-122-122-1222-12-1-12-2-1-1-12-12-12-1-2-2-2-20022-1-1-1-11-211-2-211111120-211002200-2-200-1-12200000000-101-21100-1-100-1-11120-2011000000-100
χ402222-122-122-1222-12-1-12-2-1-1-12-12-12-1-2-2-2-200-2-2-1-1-1-11-211-2-211111120211002200-2-20011-2-200000000-10-121100-1-10011-1-1-2020-1-1000000100
χ4122-2-222222-2-2-2-22-2-222202-2-2-222-2-2-2002-22-20022-2-20000000000000002-22-200002-22-200002-200000000002-22-200000000000000002-200000
χ4222-2-222222-2-2-2-22-2-222202-2-2-222-2-2-2002-2-220022-2-20000000000000002-2-2200002-2-220000-2200000000002-2-220000000000000000-2200000
χ4322-2-222222-2-2-2-22-2-222202-2-2-222-2-2-200-222-20022-2-2000000000000000-222-20000-222-20000-220000000000-222-20000000000000000-2200000
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χ4722-2-222-1221-2-21-1-2-22-1-102-211-1-111-23−3-222-200-1-111003−33−30033−3−3000-222-2−333−31-1-110000-2200−3−33300001-1-11−333−30000000000001-100000
χ4822-2-222-1221-2-21-1-2-22-1-102-211-1-111-23−3-22-2200-1-111003−33−30033−3−3000-22-22−33−331-11-100002-20033−3−300001-11-1−33−33000000000000-1100000
χ4922-2-222-1221-2-21-1-2-22-1-102-211-1-111-2−332-22-200-1-11100−33−3300−3−3330002-22-2−33−33-11-1100002-200−3−3330000-11-11−33−33000000000000-1100000
χ5022-2-222-1221-2-21-1-2-22-1-102-211-1-111-2−332-2-2200-1-11100−33−3300−3−3330002-2-22−333−3-111-10000-220033−3−30000-111-1−333−30000000000001-100000
χ5122-2-222-1221-2-21-1-2-22-1-102-211-1-111-2−33-222-200-1-11100−33−3300−3−333000-222-23−3−331-1-110000-220033−3−300001-1-113−3−330000000000001-100000
χ5222-2-222-1221-2-21-1-2-22-1-102-211-1-111-2−33-22-2200-1-11100−33−3300−3−333000-22-223−33−31-11-100002-200−3−33300001-11-13−33−3000000000000-1100000
χ532-22-2222-2-22-2-2-2-2222220-2-2-2-2-2-22220000002-22-2-220000000000000000000000000002-22-2002i−2i2i−2i2i−2i0000000000002-20000000000002i−2i000
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χ944-4-444-24-42-44-24-4-42-24-202-24-2-42-42200000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ954-4-444-24-42-44-24-4-42-24-202-24-2-42-42200000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ964-4-44-2442-4-4-244-42-4-2-2402-2-242-42-4200000000-22-2200000000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ974-4-44-2442-4-4-244-42-4-2-2402-2-242-42-4200000000-22-22000000000000000000000000000000000000000000000000000000000002i3−2i3000000000
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
χ10088-8-8-4-48-4-4-844-88442-4-402-244-4-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-44444-44422202-2-2-222-2-2-243−43000000-1-11100−2323−23230033−3−30000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-44444-44422202-2-2-222-2-2-2−4343000000-1-1110023−2323−2300−3−3330000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-84-4-84448-4-4-420444-24-2-42-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-44-8-44-844-48-42-4044-24-242-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444-44444-4-42220-2-2-2-2-2-222200000000-111-10000006-6-33-330000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-44444-4-42220-2-2-2-2-2-222200000000-111-1000000-663-33-30000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-8448-4-44-84-4-4204-4-424-24-24000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-44-84-48-444-8-42-404-42-4-24-244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4844-8-4-48-8442-4-40-22-4-44444-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-4-4-44442220-2222-2-2-2-2-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-4-4-44442220-2222-2-2-2-2-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000

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