Finite Group Databasebeta

← Group #13169371

Character table — Group #13169371

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121244441212121236661212121212121212122444661212121212121212121212121212121212121212446661212121212121212124444412121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111111111-1-111111111111111111-1-1-111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111-1111-1-11111-1-111-1-11111111111-1-1-1-1-1111-1-11111-111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-1-11-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111111-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-111-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111111-1-1-1-111-1-111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1-11-1-111111-1-1-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-11-1111-1-111-1-111-111-1-1-1-11-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1111-11-1-1-111-1-111-11-1-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1-1-1111-11-11-1-11111-1-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11-11111-1-11-11-11-1-11111-1-111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1111-1-11111-11-1-1-1-1-11111-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111111-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-1-1-111-111-1-1-1-11-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-1-111-11-1-111111-1-1-11-11-1
χ17222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-12002-1-122-1-1-1-1002222-1-1-1-1-1-1-1-1222-1-1000-1-1000020000-1-100-1-100000
χ18222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-20021122-1-11100-2-222-1-1-1-1-1-1-1-1-2-2-211000110000-2000011001100000
χ19222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-1200-2-1-1-2-211-1-10022-2-211111111-2-22-1-1000-1-10000-2000011001100000
χ20222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-200-211-2-2111100-2-2-2-21111111122-21100011000020000-1-100-1-100000
χ21222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-21111112222-1-1-1-1-1-1-1-1-2-2-2111111-200-211-2-211-1-1002222-1-1-1-1111122-211000-1-10000-20000-1-1001100000
χ22222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-211111122-2-2-1-1-1-1-1-1-1-1-2-2-2111111200-2-1-1-2-2111100-2-222-1-1-1-11111-2-22-1-1000110000200001100-1-100000
χ23222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-2111111-2-2221111-1-1-1-1-2-2-2111111-20021122-1-1-1-10022-2-21111-1-1-1-1-2-2-211000-1-10000200001100-1-100000
χ24222222-1222-12-12-122-1-1-22-12-1-1-1-1-12-2-2111111-2-2-2-21111-1-1-1-1-2-2-21111112002-1-122-1-11100-2-2-2-21111-1-1-1-1222-1-1000110000-20000-1-1001100000
χ2522222-1222-12-12-122-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1222022000022-1-1-1-1000000000000-1-1-1-122-1-1-1-1-1-10002200-1-100-10000
χ2622222-1222-12-12-122-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-12-2-202200002211-1-1000000000000-1-1-11-2-2-1-11111000-2-200110010000
χ2722222-1222-12-12-122-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2220-2-20000-2-2-1-111000000000000111-12211-1-1-1-1000-2-200110010000
χ2822222-1222-12-12-122-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20-2-20000-2-211110000000000001111-2-21111110002200-1-100-10000
χ2922222-1222-12-12-122-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-22-20-2-2000022-1-1-1-100000000000011112-2-1-1-1-111000-2200-1-10010000
χ3022222-1222-12-12-122-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-2-220-2-200002211-1-1000000000000111-1-22-1-111-1-10002-2001100-10000
χ3122222-1222-12-12-122-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111122-20220000-2-2-1-111000000000000-1-1-112-211-1-1110002-2001100-10000
χ3222222-1222-12-12-122-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-11111111112-220220000-2-21111000000000000-1-1-1-1-221111-1-1000-2200-1-10010000
χ332222-122-1-1222222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1022200-1-122002200-1-1-1-1-1-1-1-1-1-1000002-1-100-1-1-1-1022000000000-1-100
χ342222-122-1-1222222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-122002222-1-1-1-12-1-122-1-1-1-10-2-2200-1-12200-2-200-1-1-1-1-1-1-1-1-1-100000-2110011110-2-20000000001100
χ352222-122-1-1222222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1022-20011-2-20022001111111111000002-1-100-1-1-1-10-2-20000000001100
χ362222-122-1-1222222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2-20011-2-200-2-200111111111100000-211001111022000000000-1-100
χ372222-122-1-1222222-1-1-12-2-12-1-12-1-12-111-2-2111122002222-1-1-1-1-211-2-2111102-2-20011-2-2002200-1-1-1-1-1-1111100000-2-1100-1-11102-2000000000-1100
χ382222-122-1-1222222-1-1-12-2-12-1-12-1-12-111-2-2111122002222-1-1-1-1-211-2-211110-22-20011-2-200-2-200-1-1-1-1-1-111110000021-10011-1-10-220000000001-100
χ392222-122-1-1222222-1-1-12-2-12-1-12-1-12-111-2-21111-2-200-2-2-2-2-1-1-1-1-211-2-2111102-2200-1-122002200111111-1-1-1-100000-2-1100-1-1110-220000000001-100
χ402222-122-1-1222222-1-1-12-2-12-1-12-1-12-111-2-21111-2-200-2-2-2-2-1-1-1-1-211-2-211110-22200-1-12200-2-200111111-1-1-1-10000021-10011-1-102-2000000000-1100
χ4122-2-2222-2-22-2-2-2-2222220-22-2-2-22-2-22000000002-22i−2i22-2-222-2-200000000000000000002i−2i002i−2i2-222-2-200002i−2i0000002i−2i0000000002i−2i000000000
χ4222-2-2222-2-22-2-2-2-2222220-22-2-2-22-2-22000000002-2−2i2i22-2-222-2-20000000000000000000−2i2i00−2i2i2-222-2-20000−2i2i000000−2i2i000000000−2i2i000000000
χ4322-2-2222-2-22-2-2-2-2222220-22-2-2-22-2-2200000000-222i−2i-2-22222-2-200000000000000000002i−2i002i−2i-22-2-2220000−2i2i0000002i−2i000000000−2i2i000000000
χ4422-2-2222-2-22-2-2-2-2222220-22-2-2-22-2-2200000000-22−2i2i-2-22222-2-20000000000000000000−2i2i00−2i2i-22-2-22200002i−2i000000−2i2i0000000002i−2i000000000
χ4522-2-222-1-2-221-21-2-122-1-10-2-1-211-1112003−333−3−32-22i−2i-1-111-1-1110003−333−3−30000−i3i3003−3−ii002i−2i2-2-1-11133−3−32i−2i0−i3i3000−ii000000000−ii00−i3i300000
χ4622-2-222-1-2-221-21-2-122-1-10-2-1-211-1112003−333−3−32-2−2i2i-1-111-1-1110003−333−3−30000i3−i3003−3i−i00−2i2i2-2-1-11133−3−3−2i2i0i3−i3000i−i000000000i−i00i3−i300000
χ4722-2-222-1-2-221-21-2-122-1-10-2-1-211-1112003−333−3−3-222i−2i11-1-1-1-1110003−333−3−30000−i3i300−33−ii002i−2i-2211-1-1−3−333−2i2i0−i3i3000−ii000000000i−i00i3−i300000
χ4822-2-222-1-2-221-21-2-122-1-10-2-1-211-1112003−333−3−3-22−2i2i11-1-1-1-1110003−333−3−30000i3−i300−33i−i00−2i2i-2211-1-1−3−3332i−2i0i3−i3000i−i000000000−ii00−i3i300000
χ4922-2-222-1-2-221-21-2-122-1-10-2-1-211-111200−33−3−3332-22i−2i-1-111-1-111000−33−3−3330000i3−i300−33−ii002i−2i2-2-1-111−3−3332i−2i0i3−i3000−ii000000000−ii00i3−i300000
χ5022-2-222-1-2-221-21-2-122-1-10-2-1-211-111200−33−3−3332-2−2i2i-1-111-1-111000−33−3−3330000−i3i300−33i−i00−2i2i2-2-1-111−3−333−2i2i0−i3i3000i−i000000000i−i00−i3i300000
χ5122-2-222-1-2-221-21-2-122-1-10-2-1-211-111200−33−3−333-222i−2i11-1-1-1-111000−33−3−3330000i3−i3003−3−ii002i−2i-2211-1-133−3−3−2i2i0i3−i3000−ii000000000i−i00−i3i300000
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χ5344444-2-244-2-2-2-2-2-24-2-214-21-2-21-2-21-244-2-2-2-2-2-2004400001111-2-2-21111114000-2-20000-2-200-2-2000000000000-2110001100000000000000000000
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χ5544444-2-244-2-2-2-2-2-24-2-21-4-21-2-21-2-21-2-4-4222222004400001111222-1-1-1-1-1-1-4000220000-2-200-2-20000000000002-1-10001100000000000000000000
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χ574444-24-2-2-24-24-24-2-2-21-24-2-2-21-211-2-2-2-2-2-211114400-2-2-2-211114-2-2-2-21111000400-2-2-2-2000000-2-211111111000000000000000000000000000000
χ584444-24-2-2-24-24-24-2-2-21-24-2-2-21-211-2-2-2-2-2-21111-4-400222211114-2-2-2-21111000-400222200000022-1-1-1-1-1-1-1-1000000000000000000000000000000
χ594444-24-2-2-24-24-24-2-2-21-2-4-2-2-21-211-2-22222-1-1-1-14400-2-2-2-21111-42222-1-1-1-1000-4002222000000-2-21111-1-1-1-1000000000000000000000000000000
χ604444-24-2-2-24-24-24-2-2-21-2-4-2-2-21-211-2-22222-1-1-1-1-4-40022221111-42222-1-1-1-1000400-2-2-2-200000022-1-1-1-11111000000000000000000000000000000
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χ844-44-4-24-22-2-4-2-42422-21-20-222-12-11-2200003i−3i3i−3i000023−2323−231-11-1000003i−3i3i−3i000000−2i32i30000000000−33−33i3−i3i3−i3000000000000000000000000000000
χ854-44-4-24-22-2-4-2-42422-21-20-222-12-11-2200003i−3i3i−3i0000−2323−23231-11-1000003i−3i3i−3i0000002i3−2i300000000003−33−3−i3i3−i3i3000000000000000000000000000000
χ864-44-4-24-22-2-4-2-42422-21-20-222-12-11-220000−3i3i−3i3i000023−2323−231-11-100000−3i3i−3i3i0000002i3−2i30000000000−33−33−i3i3−i3i3000000000000000000000000000000
χ874-44-4-24-22-2-4-2-42422-21-20-222-12-11-220000−3i3i−3i3i0000−2323−23231-11-100000−3i3i−3i3i000000−2i32i300000000003−33−3i3−i3i3−i3000000000000000000000000000000
χ884-4-444444-4-4-444-4-4-44440-4-4444-4-4-4-400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-24-4-424-2-42-44-2-20-424-2-2222-400000000000023−23−2323-222-200000000000000000000000000023−23−23230000000000000000000000000000000000
χ904-4-4444-24-4-424-2-42-44-2-20-424-2-2222-4000000000000−232323−23-222-2000000000000000000000000000−232323−230000000000000000000000000000000000
χ914-4-444-244-42-4-242-4-4-24-2022-24-2-4-4220000000000000000-222-200000000000000000000023−23000000000000000000000023−23000000000000000000
χ924-4-444-244-42-4-242-4-4-24-2022-24-2-4-4220000000000000000-222-2000000000000000000000−23230000000000000000000000−2323000000000000000000
χ934-4-44-244-22-4-444-4-42-2-2402-4-2-2422-42−2i32i300−2i32i32i3−2i300000000-222-20−2i32i300−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ944-4-44-244-22-4-444-4-42-2-2402-4-2-2422-422i3−2i3002i3−2i3−2i32i300000000-222-202i3−2i3002i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ954-4-44-24-2-22-424-2-422-21-2022-21-2-1-122−2i32i300i3−i3−i3i3000023−23−23231-1-110−2i32i300i3−i3−i3i3000000000000000000−333−3−3i3i3i−3i000000000000000000000000000000
χ964-4-44-24-2-22-424-2-422-21-2022-21-2-1-122−2i32i300i3−i3−i3i30000−232323−231-1-110−2i32i300i3−i3−i3i30000000000000000003−3−333i−3i−3i3i000000000000000000000000000000
χ974-4-44-24-2-22-424-2-422-21-2022-21-2-1-1222i3−2i300−i3i3i3−i3000023−23−23231-1-1102i3−2i300−i3i3i3−i3000000000000000000−333−33i−3i−3i3i000000000000000000000000000000
χ984-4-44-24-2-22-424-2-422-21-2022-21-2-1-1222i3−2i300−i3i3i3−i30000−232323−231-1-1102i3−2i300−i3i3i3−i30000000000000000003−3−33−3i3i3i−3i000000000000000000000000000000
χ994-4-44-2-24-222-4-242-421-2-20-121-2-2222-1−2i32i300−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i300000000000023−230000000000000000000000−333i−3i0000000000000000
χ1004-4-44-2-24-222-4-242-421-2-20-121-2-2222-1−2i32i300−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i3000000000000−232300000000000000000000003−3−3i3i0000000000000000
χ1014-4-44-2-24-222-4-242-421-2-20-121-2-2222-12i3−2i3002i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i300000000000023−230000000000000000000000−33−3i3i0000000000000000
χ1024-4-44-2-24-222-4-242-421-2-20-121-2-2222-12i3−2i3002i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i3000000000000−232300000000000000000000003−33i−3i0000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4844-4-84-848-42-4-40-2-4-244-4442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-444-44444-4-42220-22-2-2-22-2-220043−43−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-44444-4-42220-22-2-2-22-2-2200−43432323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-884-444-44-8-4-420-4-244-24-42400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-484-4484-8-4-842-4-4024-2444-4-4-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-44-444-44422202-2-2-2-2-222-200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-44-444-44422202-2-2-2-2-222-20000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-48-844-4-444-8-4-4204-2-4-4244-2400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-4444-4-44442220-2-2222-2-2-2-2−4i34i3002i3−2i3−2i32i300000000-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-4444-4-44442220-2-2222-2-2-2-24i3−4i300−2i32i32i3−2i300000000-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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