Finite Group Databasebeta

← Group #13169422

Character table — Group #13169422

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121244444121212121212121222444444121212121212121212121212121212121212121244661212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1111111-1-1-1-1-1-111-1-11-1111-11-11111-1-11111-1-11-1-1-1-1-111-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-11-111111-1-111-1-1-1-1-1-111-1111-11-1111-1-11111-1-111-11-1-1-1-1-1-111-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-1-1-111111111-1-1-1-111-1-11111-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-11-11-1-1-111-1-1-1-111-1-1-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1-11-11-1-1-1-111-1-1-1-1111-1-1-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-111-1-111-1-1-11-1-11-1-1111-1-111-1-111-1-1-1111-1-111-1-111-11-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-1111-111-1-1-1-111111-1-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-111-1-1-1-111-11111-1-11-1-1-1-1111111-1-11-111-1-1-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-11111-1-111-1-11-111-111-1-1-111-1-111-1-111-1111-1-111-1-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1
χ17222222-1-122-122-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1022220000222222220000-1-100-1-12200-1-1-1-100-1-1-1-100-1-1-1-1000000000
χ18222222-1-122-122-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-102-22-2000022-2-2-2-2-2-20000-1100-112-200-1-11100-1-111001111000000000
χ19222222-1-122-122-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-22-220000-2-222-2-2-2-200001-1001-1-220011-1-10011-1-1001111000000000
χ20222222-1-122-122-1222-1-122-1-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-20000-2-2-2-222220000110011-2-200111100111100-1-1-1-1000000000
χ21222222-1-122-122-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-211111111022-2-200002222-2-22200001100-1-1-2-200111100-1-1-1-10011-1-1000000000
χ22222222-1-122-122-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-21111111102-2-22000022-2-222-2-200001-100-11-220011-1-100-1-11100-1-111000000000
χ23222222-1-122-122-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-2111111110-222-20000-2-22222-2-20000-11001-12-200-1-1110011-1-100-1-111000000000
χ24222222-1-122-122-1222-1-1-22-1-12-1-12-1-11100-1-1-1-1-2-2-2-2111111110-2-2220000-2-2-2-2-2-2220000-1-100112200-1-1-1-10011110011-1-1000000000
χ2522222-1222-122-122-1-12-12-12-1-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-12020222-1-100-1-100000022022-1020-1-1-100-1-1-1-100-1-102000000-1-1000-10
χ2622222-1222-122-122-1-12-12-12-1-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-120-20-222-1-10011000000-2-20-22-10-201-1-10011-1-100110-20000001100010
χ2722222-1222-122-122-1-12-12-12-1-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20202-2-21100-1-1000000-2-202-21020-11100-1-11100-1-10-20000001100010
χ2822222-1222-122-122-1-12-12-12-1-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-20-2-2-2110011000000220-2-210-20111001111001102000000-1-1000-10
χ2922222-1222-122-122-1-12-1-2-12-1-12-1-12-1-2-222-1-1-1-1-2111-2-2111111-2020-222-1-100-1-1000000220-2-210201-1-100111100-1-10-2000000-1-100010
χ3022222-1222-122-122-1-12-1-2-12-1-12-1-12-1-2-222-1-1-1-1-2111-2-2111111-20-20222-1-10011000000-2-202-210-20-1-1-100-1-11100110200000011000-10
χ3122222-1222-122-122-1-12-1-2-12-1-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111112020-2-2-21100-1-1000000-2-20-22-10201110011-1-100-1-10200000011000-10
χ3222222-1222-122-122-1-12-1-2-12-1-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-211111120-202-2-211001100000022022-10-20-11100-1-1-1-100110-2000000-1-100010
χ332222-1222-122-122-12-1-122-1-12-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-122020-1-122-1-1000000220020-1220-10-1-1-1-100-1-1-1-100200000-1-10000-100
χ342222-1222-122-122-12-1-122-1-12-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12-20-20-1-12211000000-2-200-20-12-2010-1-11100-1-11100-200000110000100
χ352222-1222-122-122-12-1-122-1-12-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2202011-2-2-1-1000000-2-200201-220-1011-1-10011-1-100-200000110000100
χ362222-1222-122-122-12-1-122-1-12-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2011-2-2110000002200-201-2-2010111100111100200000-1-10000-100
χ372222-1222-122-122-12-1-12-2-1-12-1-12-1-12-2-222-1-1-1-11-21111-2-21111-220-20-1-122-1-10000002200-201-22010-1-1110011-1-100-200000-1-10000100
χ382222-1222-122-122-12-1-12-2-1-12-1-12-1-12-2-222-1-1-1-11-21111-2-21111-2-2020-1-12211000000-2-200201-2-20-10-1-1-1-100111100200000110000-100
χ392222-1222-122-122-12-1-12-2-1-12-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111220-2011-2-2-1-1000000-2-200-20-122010111100-1-1-1-100200000110000-100
χ402222-1222-122-122-12-1-12-2-1-12-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-211112-202011-2-211000000220020-12-20-1011-1-100-1-11100-200000-1-10000100
χ4122-2-2222222-2-2-2-2-2-22220-2222-2-2-2-2-2002-222-2-2000000000000000002-22-200002-2000000000000002-20000000000002-20000002-2000
χ4222-2-2222222-2-2-2-2-2-22220-2222-2-2-2-2-2002-222-2-2000000000000000002-22-20000-22000000000000002-2000000000000-22000000-22000
χ4322-2-2222222-2-2-2-2-2-22220-2222-2-2-2-2-200-2222-2-200000000000000000-22-2200002-200000000000000-220000000000002-2000000-22000
χ4422-2-2222222-2-2-2-2-2-22220-2222-2-2-2-2-200-2222-2-200000000000000000-22-220000-2200000000000000-22000000000000-220000002-2000
χ452-22-2222-2-2-2-2222-2-22220-2-2-2-2-2-222200002-2-220000000000000000000000000002-22i−2i2i−2i0000000000000000000000002-22i−2i2i−2i00000
χ462-22-2222-2-2-2-2222-2-22220-2-2-2-2-2-222200002-2-220000000000000000000000000002-2−2i2i−2i2i0000000000000000000000002-2−2i2i−2i2i00000
χ472-22-2222-2-2-2-2222-2-22220-2-2-2-2-2-222200002-2-22000000000000000000000000000-222i−2i−2i2i000000000000000000000000-222i−2i−2i2i00000
χ482-22-2222-2-2-2-2222-2-22220-2-2-2-2-2-222200002-2-22000000000000000000000000000-22−2i2i2i−2i000000000000000000000000-22−2i2i2i−2i00000
χ4944444-2-2-24-2-24-2-24-2-2-214-2-21-2-21-2-21-2-20011114-2-2-2-2-211111100404000000-2-2000000000-2000-20-2000011000011000000000000000
χ5044444-2-2-24-2-24-2-24-2-2-214-2-21-2-21-2-21-2-20011114-2-2-2-2-211111100-40-40000002200000000020002020000-1-10000-1-1000000000000000
χ5144444-2-2-24-2-24-2-24-2-2-21-4-2-21-2-21-2-2122001111-422222-1-1-1-1-1-10040-4000000-2-20000000002000-2020000-1-1000011000000000000000
χ5244444-2-2-24-2-24-2-24-2-2-21-4-2-21-2-21-2-2122001111-422222-1-1-1-1-1-100-40400000022000000000-200020-20000110000-1-1000000000000000
χ534444-24-2-2-24-2-24-2-24-21-24-21-2-21-2-21-2-2-2001111-24-2-211-2-21111040400000-2-20000000000-2000-20-20001100001100000000000000000
χ544444-24-2-2-24-2-24-2-24-21-24-21-2-21-2-21-2-2-2001111-24-2-211-2-211110-40-4000002200000000002000202000-1-10000-1-100000000000000000
χ554444-24-2-2-24-2-24-2-24-21-2-4-21-2-21-2-21-2220011112-422-1-122-1-1-1-1040-400000-2-200000000002000-202000-1-100001100000000000000000
χ564444-24-2-2-24-2-24-2-24-21-2-4-21-2-21-2-21-2220011112-422-1-122-1-1-1-10-40400000220000000000-200020-2000110000-1-100000000000000000
χ574444-2-244-2-24-2-24-2-21-2-241-2-21-2-21-2-244441111-2-211-2-2-2-2111140000-2-2-2-200000000000000-2-20000110000110000000000000000000
χ584444-2-244-2-24-2-24-2-21-2-241-2-21-2-21-2-244-4-41111-2-211-2-2-2-21111-40000222200000000000000220000-1-10000-1-10000000000000000000
χ594444-2-244-2-24-2-24-2-21-2-2-41-2-21-2-21-2-2-4-444111122-1-12222-1-1-1-1-40000-2-2-2-200000000000000220000110000-1-10000000000000000000
χ604444-2-244-2-24-2-24-2-21-2-2-41-2-21-2-21-2-2-4-4-4-4111122-1-12222-1-1-1-140000222200000000000000-2-20000-1-10000110000000000000000000
χ6144-4-444-2-2442-4-42-4-44-2-20-4-2-2422-4220000-2-22200000000000000000000000004-40000000000000000000000000000-2200000000000
χ6244-4-444-2-2442-4-42-4-44-2-20-4-2-2422-4220000-2-2220000000000000000000000000-4400000000000000000000000000002-200000000000
χ6344-4-44-2444-2-4-42-4-42-24-2024-2-2-422-42004-4-2-222000000000000000004-4-2200000000000000000000-220000000000000000000000000
χ6444-4-44-2444-2-4-42-4-42-24-2024-2-2-422-4200-44-2-22200000000000000000-442-2000000000000000000002-20000000000000000000000000
χ6544-4-4-2444-24-42-4-42-4-2-2402-24-22-422-4004-4-2-22200000000000000000-224-400000000000000000000-220000000000000000000000000
χ6644-4-4-2444-24-42-4-42-4-2-2402-24-22-422-400-44-2-222000000000000000002-2-44000000000000000000002-20000000000000000000000000
χ6744-4-4-2-244-2-2-422-4221-2-20-1-2-2122-122004-411-1-1003i−3i00003i3i−3i−3i00000-22-22000000000000000000001-100003i−3i0000000000000000000
χ6844-4-4-2-244-2-2-422-4221-2-20-1-2-2122-122004-411-1-100−3i3i0000−3i−3i3i3i00000-22-22000000000000000000001-10000−3i3i0000000000000000000
χ6944-4-4-2-244-2-2-422-4221-2-20-1-2-2122-12200-4411-1-1003i−3i00003i3i−3i−3i000002-22-200000000000000000000-110000−3i3i0000000000000000000
χ7044-4-4-2-244-2-2-422-4221-2-20-1-2-2122-12200-4411-1-100−3i3i0000−3i−3i3i3i000002-22-200000000000000000000-1100003i−3i0000000000000000000
χ714-44-444-22-4-4244-2-4-44-2-20-422-4224-2-20000-222-20000000000000000000000000004-40000000000000000000000000000-22000000000
χ724-44-444-22-4-4244-2-4-44-2-20-422-4224-2-20000-222-2000000000000000000000000000-4400000000000000000000000000002-2000000000
χ734-44-44-24-4-42-44-24-42-24-202-422-42-24-20000-222-200000000000000000000000000000004i−4i0000000000000000000000000000−2i2i00000
χ744-44-44-24-4-42-44-24-42-24-202-422-42-24-20000-222-20000000000000000000000000000000−4i4i00000000000000000000000000002i−2i00000
χ754-44-4-244-42-4-4-2442-4-2-24022-422-4-2-240000-222-2000000000000000000000000000004i−4i0000000000000000000000000000−2i2i0000000
χ764-44-4-244-42-4-4-2442-4-2-24022-422-4-2-240000-222-200000000000000000000000000000−4i4i00000000000000000000000000002i−2i0000000
χ774-4-44444-4-4-44-4-4-44444404-4-4-444-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ784-4-4444-22-4-4-2-4-42444-2-20422-4-2-2-42223−2300-22-22000023−2323−2323−2323−2300000000000000000000000000000000000000000000000000000000
χ794-4-4444-22-4-4-2-4-42444-2-20422-4-2-2-422−232300-22-220000−2323−2323−2323−232300000000000000000000000000000000000000000000000000000000
χ804-4-444-24-4-424-42-44-2-24-20-2-4224-22-420000-22-220000000000000000000000023−230000000000000000000000000023−23000000000000000
χ814-4-444-24-4-424-42-44-2-24-20-2-4224-22-420000-22-2200000000000000000000000−232300000000000000000000000000−2323000000000000000
χ824-4-444-2-22-42-2-4224-2-2-210-22-12-2122-123−23001-11-1000023−23−33−33−330000000000023−23000000000000000000003-30000−33000000000000000
χ834-4-444-2-22-42-2-4224-2-2-210-22-12-2122-123−23001-11-1000023−23−33−33−3300000000000−232300000000000000000000-3300003−3000000000000000
χ844-4-444-2-22-42-2-4224-2-2-210-22-12-2122-1−2323001-11-10000−23233−33−33−30000000000023−2300000000000000000000-330000−33000000000000000
χ854-4-444-2-22-42-2-4224-2-2-210-22-12-2122-1−2323001-11-10000−23233−33−33−300000000000−2323000000000000000000003-300003−3000000000000000
χ864-4-44-244-42-442-4-4-24-2-240-22-42-2422-40000-22-2200000000000000000000023−230000000000000000000000000023−2300000000000000000
χ874-4-44-244-42-442-4-4-24-2-240-22-42-2422-40000-22-22000000000000000000000−232300000000000000000000000000−232300000000000000000
χ884-4-44-24-222-4-22-42-24-21-20-2-1221-22-1223−23001-11-10000−3323−23−33−3300000000023−23000000000000000000003-30000−3300000000000000000
χ894-4-44-24-222-4-22-42-24-21-20-2-1221-22-1223−23001-11-10000−3323−23−33−33000000000−232300000000000000000000-3300003−300000000000000000
χ904-4-44-24-222-4-22-42-24-21-20-2-1221-22-12−2323001-11-100003−3−23233−33−300000000023−2300000000000000000000-330000−3300000000000000000
χ914-4-44-24-222-4-22-42-24-21-20-2-1221-22-12−2323001-11-100003−3−23233−33−3000000000−2323000000000000000000003-300003−300000000000000000
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
χ9488-8-88-4-4-48-44-844-84-4-4204-42-44-244-2000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-48-4-4-4844-844-8-42-4042-4-4-244-24000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4-4-4-44444442220-2222-2-2-2-2-20000-1-111006i−6i0000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4-4-4-44444442220-2222-2-2-2-2-20000-1-11100−6i6i00003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ988-88-88-4-44-8448-4-4-84-4-42044-244-2-4-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-48-444-84-48-44-8-42-404-244-24-42-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-48-844-8-4-48442-4-40-244-2442-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-44444-4-4-4442220-2-2-2-2-2-22220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-44444-4-4-4442220-2-2-2-2-2-22220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48-844844-8-4-42-4-40244-2-4-4-24400002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4444-4444-4-422202-2-2-222-2-2-243−4300-11-110000−2323−23233−33−300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4444-4444-4-422202-2-2-222-2-2-2−434300-11-11000023−2323−23−33−3300000000000000000000000000000000000000000000000000000000

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