Finite Group Databasebeta

← Group #13169433

Character table — Group #13169433

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212124444412121212121212124444444412121212121212121212121212121212121212124412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-1-1-1-1-11111-11-1-1111111-1-11111-1-1-11-1-1-1-1-1-111-1-1-11-1
χ31111111111111111111111111111111111111111111111111-111-111111-1-11111-1-1-1-1-1-11-11-1111-111-1-11111-1-1111-1-1-1-1-111-1-1-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-11-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-11111-1-11111-1-1-111111-11-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-111-1-1-1-1-1-1-11-11-1-1-11-1-111-1-1-1-111-1-11-1-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-1-1-111-1-11-111-1-1-1-1-1-111-1-1-1-111-11-1-1-1-1-1-11111-111
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-11111-1-1-1111-1-1111111-1-1-1-1-1-11-111-1-1-1-111111-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-1111-1-111-1-111-1-111-1-111-1-1-1-1-1-1111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1111-1-111-1-111-11-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-111-1-11-1-11111-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-11111-1-111-1-1-1-11-111-1-11-1-1-111-1-111-1-11111-1-111-1-1-1-11111-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111111-1-1-111-1-1-1-1-1-11111111-111-1-1-1-111-1-11-11
χ17222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-12202200002222002222000-1-1-1-120200-1-1-1-100-1-1-1-100-1-1-1-1000000000
χ18222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-12-202-2000022-2-200-2-2-2-2000-11-11-20200-1-11100-1-111001111000000000
χ19222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-220-220000-2-22200-2-2-2-20001-11-120-20011-1-10011-1-1001111000000000
χ20222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-2-20-2-20000-2-2-2-20022220001111-20-200111100111100-1-1-1-1000000000
χ21222222-12222-1-1-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-211111111220-2-2000022-2-200-2-22200011-1-120-200-1-1-1-100111100-1-111000000000
χ22222222-12222-1-1-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-2111111112-20-22000022220022-2-20001-1-11-20-200-1-1110011-1-10011-1-1000000000
χ23222222-12222-1-1-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2202-20000-2-2-2-20022-2-2000-111-12020011-1-100-1-1110011-1-1000000000
χ24222222-12222-1-1-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2-20220000-2-22200-2-222000-1-111-20200111100-1-1-1-100-1-111000000000
χ2522222-1222-1-1222-12-12-12-12-1-12-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-10220222-1-100-1-122000000-10202-120-1-100-1-1-1-100-1-1200000-1-10000-100
χ2622222-1222-1-1222-12-12-12-12-1-12-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-10-220-222-1-10011-2-2000000-10-20-2120-1-10011-1-10011-200000110000100
χ2722222-1222-1-1222-12-12-12-12-1-12-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-102-202-2-21100-1-1-2-200000010202-1-201100-1-11100-1-1-200000110000100
χ2822222-1222-1-1222-12-12-12-12-1-12-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-2-20-2-2-21100112200000010-20-21-20110011110011200000-1-10000-100
χ2922222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-222-1-1-1-11-211-2-211111102-20-222-1-10011-2-200000010-202-1-20-1-100-1-1110011200000110000-100
χ3022222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-222-1-1-1-11-211-2-21111110-2-20222-1-100-1-1220000001020-21-20-1-100111100-1-1-200000-1-10000100
χ3122222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-2-2-2-1-1-1-11-211-2-21111110220-2-2-211001122000000-10-202-1201100-1-1-1-10011-200000-1-10000100
χ3222222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-2-2-2-1-1-1-11-211-2-21111110-2202-2-21100-1-1-2-2000000-1020-2120110011-1-100-1-1200000110000-100
χ332222-122-1-1222222-1-1-122-1-12-1-12-1-122222-1-1-1-12-1-1-1-1-122-1-1-1-120220-1-122-1-10000000022220200-1-1-1-1-1-100-1-1-1-10002000000-1-1000-10
χ342222-122-1-1222222-1-1-122-1-12-1-12-1-122222-1-1-1-12-1-1-1-1-122-1-1-1-1-202-20-1-1221100000000-2-22-20-200-11-1-11100-1-111000-20000001100010
χ352222-122-1-1222222-1-1-122-1-12-1-12-1-1222-2-2-1-1-1-12-1-1-1-1-122-1-1-1-120-22011-2-2-1-100000000-2-2-2202001-111-1-10011-1-1000-20000001100010
χ362222-122-1-1222222-1-1-122-1-12-1-12-1-1222-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-2011-2-2110000000022-2-20-2001111110011110002000000-1-1000-10
χ372222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-222-1-1-1-1-211111-2-2111120-2-20-1-122-1-10000000022-2-2020011-1-1-1-1001111000-2000000-1-100010
χ382222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-222-1-1-1-1-211111-2-21111-20-220-1-1221100000000-2-2-220-2001-1-1-1110011-1-1000200000011000-10
χ392222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-2-2-2-1-1-1-1-211111-2-21111202-2011-2-2-1-100000000-2-22-20200-1111-1-100-1-111000200000011000-10
χ402222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-2-2-2-1-1-1-1-211111-2-21111-2022011-2-2110000000022220-200-1-1111100-1-1-1-1000-2000000-1-100010
χ412-22-22222-22-2-22-2-2-22220-2222-2-2-2-2-2002-222-2-2000000000000000002-22-2000000002-200000000002-20000000000002-20000002-2000
χ422-22-22222-22-2-22-2-2-22220-2222-2-2-2-2-2002-222-2-2000000000000000002-22-200000000-2200000000002-2000000000000-22000000-22000
χ432-22-22222-22-2-22-2-2-22220-2222-2-2-2-2-200-2222-2-200000000000000000-22-22000000002-20000000000-220000000000002-2000000-22000
χ442-22-22222-22-2-22-2-2-22220-2222-2-2-2-2-200-2222-2-200000000000000000-22-2200000000-220000000000-22000000000000-220000002-2000
χ452-2-22222-2-2-222-2-2-222220-2-2-2-2-2-222200002-2-2200000000000000000000000002i−2i2i−2i002-20000000000000000000000002i−2i2i−2i2-200000
χ462-2-22222-2-2-222-2-2-222220-2-2-2-2-2-222200002-2-2200000000000000000000000002i−2i−2i2i00-22000000000000000000000000−2i2i2i−2i-2200000
χ472-2-22222-2-2-222-2-2-222220-2-2-2-2-2-222200002-2-220000000000000000000000000−2i2i2i−2i00-220000000000000000000000002i−2i−2i2i-2200000
χ482-2-22222-2-2-222-2-2-222220-2-2-2-2-2-222200002-2-220000000000000000000000000−2i2i−2i2i002-2000000000000000000000000−2i2i−2i2i2-200000
χ4944444-2-244-2-2-2-2-2-24-2-214-2-21-2-21-2-21-2-2001111-24-2-2-2-211111104004000000-2-20000000000-20-2-200000011000011000000000000000
χ5044444-2-244-2-2-2-2-2-24-2-214-2-21-2-21-2-21-2-2001111-24-2-2-2-21111110-400-40000002200000000002022000000-1-10000-1-1000000000000000
χ5144444-2-244-2-2-2-2-2-24-2-21-4-2-21-2-21-2-21220011112-42222-1-1-1-1-1-10400-400000022000000000020-2-2000000110000-1-1000000000000000
χ5244444-2-244-2-2-2-2-2-24-2-21-4-2-21-2-21-2-21220011112-42222-1-1-1-1-1-10-4004000000-2-20000000000-2022000000-1-1000011000000000000000
χ534444-24-2-2-244-2-2-24-2-21-24-21-2-21-2-21-2-2-20011114-2-2-211-2-21111400400000-2-200000000000-20-2000-2001100001100000000000000000
χ544444-24-2-2-244-2-2-24-2-21-24-21-2-21-2-21-2-2-20011114-2-2-211-2-21111-400-4000002200000000000202000200-1-10000-1-100000000000000000
χ554444-24-2-2-244-2-2-24-2-21-2-4-21-2-21-2-21-222001111-4222-1-122-1-1-1-1400-400000-2-20000000000020-2000200110000-1-100000000000000000
χ564444-24-2-2-244-2-2-24-2-21-2-4-21-2-21-2-21-222001111-4222-1-122-1-1-1-1-4004000002200000000000-202000-200-1-100001100000000000000000
χ574444-2-24-2-2-2-2444-2-21-2-241-2-21-2-21-2-244441111-2-211-2-2-2-2111100400-2-2-2-2000000000000-200000-20110000110000000000000000000
χ584444-2-24-2-2-2-2444-2-21-2-241-2-21-2-21-2-244-4-41111-2-211-2-2-2-2111100-400222200000000000020000020-1-10000-1-10000000000000000000
χ594444-2-24-2-2-2-2444-2-21-2-2-41-2-21-2-21-2-2-4-444111122-1-12222-1-1-1-100-400-2-2-2-200000000000020000020110000-1-10000000000000000000
χ604444-2-24-2-2-2-2444-2-21-2-2-41-2-21-2-21-2-2-4-4-4-4111122-1-12222-1-1-1-1004002222000000000000-200000-20-1-10000110000000000000000000
χ6144-4-4444-44-4-4-4-444-444404-4-4-444-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-2-44-4-422-24-44-2-20422-4-2-2-42223−2300-22-22000023−2323−232323−23−2300000000000000000000000000000000000000000000000000000000
χ6344-4-444-2-44-4-422-24-44-2-20422-4-2-2-422−232300-22-220000−2323−2323−23−23232300000000000000000000000000000000000000000000000000000000
χ6444-4-44-24-4422-4-44-2-4-24-20-2-4224-22-420000-22-220000000000000000000000023−230000000000000000000000000023−23000000000000000
χ6544-4-44-24-4422-4-44-2-4-24-20-2-4224-22-420000-22-2200000000000000000000000−232300000000000000000000000000−2323000000000000000
χ6644-4-44-2-2-442222-2-2-4-2-210-22-12-2122-123−23001-11-1000023−23−33−3−3330000000000023−23000000000000000000003-30000−33000000000000000
χ6744-4-44-2-2-442222-2-2-4-2-210-22-12-2122-123−23001-11-1000023−23−33−3−33300000000000−232300000000000000000000-3300003−3000000000000000
χ6844-4-44-2-2-442222-2-2-4-2-210-22-12-2122-1−2323001-11-10000−23233−333−3−30000000000023−2300000000000000000000-330000−33000000000000000
χ6944-4-44-2-2-442222-2-2-4-2-210-22-12-2122-1−2323001-11-10000−23233−333−3−300000000000−2323000000000000000000003-300003−3000000000000000
χ7044-4-4-2442-2-4-4-4-4442-2-240-22-42-2422-40000-22-22000000000000000000000−2i32i300000000000000000000−2i32i300000000000000000000000
χ7144-4-4-2442-2-4-4-4-4442-2-240-22-42-2422-40000-22-220000000000000000000002i3−2i3000000000000000000002i3−2i300000000000000000000000
χ7244-4-4-24-22-2-4-422-242-21-20-2-1221-22-1223−23001-11-10000−3323−23−3−333000000000−2i32i300000000000000000000i3−i300003i−3i00000000000000000
χ7344-4-4-24-22-2-4-422-242-21-20-2-1221-22-1223−23001-11-10000−3323−23−3−3330000000002i3−2i300000000000000000000−i3i30000−3i3i00000000000000000
χ7444-4-4-24-22-2-4-422-242-21-20-2-1221-22-12−2323001-11-100003−3−232333−3−3000000000−2i32i300000000000000000000i3−i30000−3i3i00000000000000000
χ7544-4-4-24-22-2-4-422-242-21-20-2-1221-22-12−2323001-11-100003−3−232333−3−30000000002i3−2i300000000000000000000−i3i300003i−3i00000000000000000
χ764-44-444-24-44-42-22-4-44-2-20-4-2-2422-4220000-2-222000000000000000000000000000004-4000000000000000000000000-2200000000000
χ774-44-444-24-44-42-22-4-44-2-20-4-2-2422-4220000-2-22200000000000000000000000000000-440000000000000000000000002-200000000000
χ784-44-44-244-4-22-44-42-4-24-2024-2-2-422-42004-4-2-222000000000000000004-4-2200000000000000000000-220000000000000000000000000
χ794-44-44-244-4-22-44-42-4-24-2024-2-2-422-4200-44-2-22200000000000000000-442-2000000000000000000002-20000000000000000000000000
χ804-44-4-244-224-4-44-4-42-2-2402-24-22-422-4004-4-2-22200000000000000000-224-400000000000000000000-220000000000000000000000000
χ814-44-4-244-224-4-44-4-42-2-2402-24-22-422-400-44-2-222000000000000000002-2-44000000000000000000002-20000000000000000000000000
χ824-44-4-2-24-22-22-44-4221-2-20-1-2-2122-122004-411-1-1003i−3i00003i−3i3i−3i00000-22-22000000000000000000001-100003i−3i0000000000000000000
χ834-44-4-2-24-22-22-44-4221-2-20-1-2-2122-122004-411-1-100−3i3i0000−3i3i−3i3i00000-22-22000000000000000000001-10000−3i3i0000000000000000000
χ844-44-4-2-24-22-22-44-4221-2-20-1-2-2122-12200-4411-1-1003i−3i00003i−3i3i−3i000002-22-200000000000000000000-110000−3i3i0000000000000000000
χ854-44-4-2-24-22-22-44-4221-2-20-1-2-2122-12200-4411-1-100−3i3i0000−3i3i−3i3i000002-22-200000000000000000000-1100003i−3i0000000000000000000
χ864-4-4444-2-4-4-44-222-444-2-20-422-4224-2-20000-222-20000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000000
χ874-4-4444-2-4-4-44-222-444-2-20-422-4224-2-20000-222-2000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000000
χ884-4-444-24-4-42-24-4-424-24-202-422-42-24-20000-222-200000000000000000000000004i−4i00000000000000000000000000000000−2i2i0000000
χ894-4-444-24-4-42-24-4-424-24-202-422-42-24-20000-222-20000000000000000000000000−4i4i000000000000000000000000000000002i−2i0000000
χ904-4-44-24422-444-4-4-4-2-2-24022-422-4-2-240000-222-200000000000000000000000000000004-40000000000000000000000000000-2200000
χ914-4-44-24422-444-4-4-4-2-2-24022-422-4-2-240000-222-20000000000000000000000000000000-4400000000000000000000000000002-200000
χ928888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-484-444-8-88-442-4-40244-2-4-4-24400002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-44444-4-4422202-2-2-222-2-2-243−4300-11-110000−2323−232333−3−300000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-44-44444-4-4422202-2-2-222-2-2-2−434300-11-11000023−2323−23−3−33300000000000000000000000000000000000000000000000000000000
χ978-88-88-4-48-8-444-444-8-4-4204-42-44-244-2000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-48-4-448-84-44-84-42-4042-4-4-244-24000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-44-444-44442220-2222-2-2-2-2-20000-1-111006i−6i0000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4-44-444-44442220-2222-2-2-2-2-20000-1-11100−6i6i00003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1018-8-888-4-4-8-84-4-44448-4-42044-244-2-4-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-444-88-444-8-4-42-404-244-24-42-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48444-48-8-84-42-4-40-244-2442-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4444-4-4444-42220-2-2-2-2-2-22220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4444-4-4444-42220-2-2-2-2-2-22220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000

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