Finite Group Databasebeta

← Group #13169448

Character table — Group #13169448

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222444444444444466668888888888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363636363636363654545454727272
order1222333666666666333466666666644443666121212121212121212121212124444121212121212121212121212444412121212121212121212121212121212121244441212121212124444121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-1-1-111-11-1111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11
χ31111111111111111111111111111111-1-111111111111111111-1111-1-1-1-111111111-1-111-111-11111-1-111-1-111111-1-1-111-1-1-1-1-1-1-1-11-1-1
χ41111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-111-1-111-1-111-1-1-11-1-1-1111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-11111-11-1
χ511111111111111111111111111111-1-111111111111111111111-1111111-1-111-1-11111-1-11-1111-1-1-111-1-1111111-1-1-11-1-111-1-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-111111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1-11-1-1-111-1-1-1-111111-1-1
χ711111111111111111111111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111111-1-11
χ811111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111
χ91111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111111-1-1-1-111-1-1-1-11-1-1-11111-1-111-1-1-11-1111-1-11111-1-1-11-1
χ101111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1-1
χ111111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1111111-1-111111-1-111-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-111-1-11
χ121111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-11111-1-1-1-11-111-1-1-1-1-1-11111-1-1111-111-1-1-1-1-1-111-1-1111
χ131111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-111-1-11-111-1-1-1-1-1-1-1-111111
χ141111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1111111-111-1-111111-1-1-1-1-1-111-1-11-11111-1-111-1-1-1-11
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-111-1-111-111111-1-1-1-11111-1-111-1-1-1-1111111-1-11-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1111-1-1-1-111-1-111-11-1111-1-111-1-111-11-1
χ17222222-1222-1-12-1222-1-122-1-1-12-12-1-12200-1-1-1-122-1-1-122-1-1-1-1-1-10222000022-1-1-1-12200220-1-1022-1-100-1-100-1-1-1-12000-1-100000000-100
χ18222222-1222-1-12-1222-1-122-1-1-12-12-1-12200-1-1-1-122-1-1-122-1-1-1-1-1-102-2-200002211-1-1-2-200-2-20-110-22-1-100-1-1001111-20001100000000100
χ19222222-1222-1-12-1222-1-122-1-1-12-12-1-1-2-200-1-1-1-122-1-1-122-1-1-1-1-1-10-2220000-2-2-1-1112200-2-201-102-211001100-1-1-1-1-20001100000000100
χ20222222-1222-1-12-1222-1-122-1-1-12-12-1-1-2-200-1-1-1-122-1-1-122-1-1-1-1-1-10-2-2-20000-2-21111-2-200220110-2-21100110011112000-1-100000000-100
χ21222222-1222-1-12-1222-1-1-22-1-1-12-12-1-12200-1-1-1-1-2-2111-2-21111110-22-2000022-1-1-1-1-2-2002201102-21100-1-100-1-111-2000-1-100000000100
χ22222222-1222-1-12-1222-1-1-22-1-1-12-12-1-12200-1-1-1-1-2-2111-2-21111110-2-2200002211-1-12200-2-201-10-2-21100-1-10011-1-120001100000000-100
χ23222222-1222-1-12-1222-1-1-22-1-1-12-12-1-1-2-200-1-1-1-1-2-2111-2-2111111022-20000-2-2-1-111-2-200-2-20-11022-1-1001100-1-11120001100000000-100
χ24222222-1222-1-12-1222-1-1-22-1-1-12-12-1-1-2-200-1-1-1-1-2-2111-2-211111102-220000-2-211112200220-1-10-22-1-100110011-1-1-2000-1-100000000100
χ2522222-122-1222-12-12-12-12-12-1-1-12-12-10022-1-1-1-12-12-1-1-1-122-1-1-1-1202222-1-1002200-1-12200202-1-1000-1-100-1-1-1-1-1-1000200-1-10000000-10
χ2622222-122-1222-12-12-12-12-12-1-1-12-12-10022-1-1-1-12-12-1-1-1-122-1-1-1-120-2-222-1-100-2-20011-2-20020-2-11000-1-100-1-11111000-20011000000010
χ2722222-122-1222-12-12-12-12-12-1-1-12-12-100-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-2022-2-211002200-1-1-2-200-2021-1000110011-1-1-1-1000-20011000000010
χ2822222-122-1222-12-12-12-12-12-1-1-12-12-100-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-20-2-2-2-21100-2-200112200-20-2110001100111111000200-1-10000000-10
χ2922222-122-1222-12-12-12-1-2-12-1-1-12-12-10022-1-1-1-1-21-21111-2-21111-202-222-1-100220011-2-200-20-21-1000-1-10011-1-111000200110000000-10
χ3022222-122-1222-12-12-12-1-2-12-1-1-12-12-10022-1-1-1-1-21-21111-2-21111-20-2222-1-100-2-200-1-12200-20211000-1-1001111-1-1000-200-1-1000000010
χ3122222-122-1222-12-12-12-1-2-12-1-1-12-12-100-2-2-1-1-1-1-21-21111-2-21111202-2-2-21100220011220020-2-1-10001100-1-1-1-111000-200-1-1000000010
χ3222222-122-1222-12-12-12-1-2-12-1-1-12-12-100-2-2-1-1-1-1-21-21111-2-2111120-22-2-21100-2-200-1-1-2-200202-110001100-1-111-1-1000200110000000-10
χ332222-122-12-122222-1-1-122-1-122-1-1-1-122222-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-122-1-10022000000-12020-1-1-1-1-1-1-1-1-1000002200000-1-1000000-1
χ342222-122-12-122222-1-1-122-1-122-1-1-1-1222-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-1-220011-2-2-1-10022000000120-20-1-1-111-1-11100000-2-200000110000001
χ352222-122-12-122222-1-1-122-1-122-1-1-1-12-2-222-1-1-1-1-12222-1-1-1-1-1-1-1-12-200-1-1221100-2-2000000-1-2020111-1-111-1-100000-2-200000110000001
χ362222-122-12-122222-1-1-122-1-122-1-1-1-12-2-2-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-20011-2-21100-2-20000001-20-20111111111000002200000-1-1000000-1
χ372222-122-12-122222-1-1-12-2-1-122-1-1-1-122222-1-1-1-11-2-2-2-211111111-2-200-1-122-1-100220000001-20-20111-1-1-1-111000002-200000-1-10000001
χ382222-122-12-122222-1-1-12-2-1-122-1-1-1-1222-2-2-1-1-1-11-2-2-2-2111111112-20011-2-2-1-10022000000-1-202011111-1-1-1-100000-220000011000000-1
χ392222-122-12-122222-1-1-12-2-1-122-1-1-1-12-2-222-1-1-1-11-2-2-2-211111111-2200-1-1221100-2-2000000120-20-1-1-1-1-1111100000-220000011000000-1
χ402222-122-12-122222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-1-1-1-11-2-2-2-211111111220011-2-21100-2-2000000-12020-1-1-11111-1-1000002-200000-1-10000001
χ412-22-222222-22-2-2-2-2-22220-222-22-2-2-2-2002-222-2-2000000000000000002-22-200000000002-2000000002-20000000000002-200002-200000
χ422-22-222222-22-2-2-2-2-22220-222-22-2-2-2-2002-222-2-2000000000000000002-22-20000000000-22000000002-2000000000000-220000-2200000
χ432-22-222222-22-2-2-2-2-22220-222-22-2-2-2-200-2222-2-200000000000000000-22-2200000000002-200000000-220000000000002-20000-2200000
χ442-22-222222-22-2-2-2-2-22220-222-22-2-2-2-200-2222-2-200000000000000000-22-220000000000-2200000000-22000000000000-2200002-200000
χ452-2-22222-2-2-2-22-2-22222202-2-2-2-22-2-222i−2i002-22-20000000000000000000002i−2i002i−2i002i−2i0000000000002i−2i0000000000002i−2i00002-2000
χ462-2-22222-2-2-2-22-2-22222202-2-2-2-22-2-222i−2i002-22-20000000000000000000002i−2i002i−2i00−2i2i0000000000002i−2i000000000000−2i2i0000-22000
χ472-2-22222-2-2-2-22-2-22222202-2-2-2-22-2-22−2i2i002-22-2000000000000000000000−2i2i00−2i2i002i−2i000000000000−2i2i0000000000002i−2i0000-22000
χ482-2-22222-2-2-2-22-2-22222202-2-2-2-22-2-22−2i2i002-22-2000000000000000000000−2i2i00−2i2i00−2i2i000000000000−2i2i000000000000−2i2i00002-2000
χ4944444-2-24-24-2-2-2-2-24-2-214-2-211-2-2-2-21000011114-2-211-2-2-2-211110044000000-2-200-2-2000000-20-2000000000111100000000000000000
χ5044444-2-24-24-2-2-2-2-24-2-214-2-211-2-2-2-21000011114-2-211-2-2-2-2111100-4-4000000220022000000202000000000-1-1-1-100000000000000000
χ5144444-2-24-24-2-2-2-2-24-2-21-4-2-211-2-2-2-2100001111-422-1-12222-1-1-1-1004-4000000-2-2002200000020-200000000011-1-100000000000000000
χ5244444-2-24-24-2-2-2-2-24-2-21-4-2-211-2-2-2-2100001111-422-1-12222-1-1-1-100-440000002200-2-2000000-202000000000-1-11100000000000000000
χ534444-24-2-24-2-2-24-24-2-21-24-21-2-2-21-21-244001111-24-2-2-2-2-211111104000000-2-200-2-20000000-2000-211001100000000000000000000000
χ544444-24-2-24-2-2-24-24-2-21-24-21-2-2-21-21-2-4-4001111-24-2-2-2-2-21111110-4000000220022000000020002-1-100-1-100000000000000000000000
χ554444-24-2-24-2-2-24-24-2-21-2-4-21-2-2-21-21-2440011112-422222-1-1-1-1-1-10-4000000-2-200-2-2000000020002-1-1001100000000000000000000000
χ564444-24-2-24-2-2-24-24-2-21-2-4-21-2-2-21-21-2-4-40011112-422222-1-1-1-1-1-1040000002200220000000-2000-21100-1-100000000000000000000000
χ574444-2-24-2-2-244-24-2-21-2-241-2-2-21-21-2-200441111-2-24-2-211-2-211114000-2-2-2-2000000000000-200-20000110011000000000000000000000
χ584444-2-24-2-2-244-24-2-21-2-241-2-2-21-21-2-200-4-41111-2-24-2-211-2-21111-4000222200000000000020020000-1-100-1-1000000000000000000000
χ594444-2-24-2-2-244-24-2-21-2-2-41-2-2-21-21-2-20044111122-422-1-122-1-1-1-1-4000-2-2-2-2000000000000200200001100-1-1000000000000000000000
χ604444-2-24-2-2-244-24-2-21-2-2-41-2-2-21-21-2-200-4-4111122-422-1-122-1-1-1-140002222000000000000-200-20000-1-10011000000000000000000000
χ6144-4-4444-4-44-4-444-4-44440-4-4-44-4-444-400004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-2-4-44224-2-4-44-2-20-422-2-424-220000-222-20000000000000000000000023−23000000000000000000000023−230000000000000000000
χ6344-4-444-2-4-44224-2-4-44-2-20-422-2-424-220000-222-200000000000000000000000−23230000000000000000000000−23230000000000000000000
χ6444-4-44-24-424-4-4-242-4-24-202-42-22-4-2420000-222-200000000000000000000000000023−230000000000000000000023−2300000000000000000
χ6544-4-44-24-424-4-4-242-4-24-202-42-22-4-2420000-222-2000000000000000000000000000−232300000000000000000000−232300000000000000000
χ6644-4-44-2-2-42422-2-22-4-2-21022-1122-2-2-100001-1-110003-3000033-3-3000000000023−230023−23000000000000000000−33−3300000000000000000
χ6744-4-44-2-2-42422-2-22-4-2-21022-1122-2-2-100001-1-110003-3000033-3-30000000000−232300−23230000000000000000003−33−300000000000000000
χ6844-4-44-2-2-42422-2-22-4-2-21022-1122-2-2-100001-1-11000-330000-3-333000000000023−2300−2323000000000000000000−333−300000000000000000
χ6944-4-44-2-2-42422-2-22-4-2-21022-1122-2-2-100001-1-11000-330000-3-3330000000000−23230023−230000000000000000003−3−3300000000000000000
χ7044-4-4-2442-4-2-4-444-42-2-24022-4422-2-2-40000-222-20000000000000000000000000000000000000000000000000000000000023−230000000
χ7144-4-4-2442-4-2-4-444-42-2-24022-4422-2-2-40000-222-200000000000000000000000000000000000000000000000000000000000−23230000000
χ724-44-444-244-4-22-42-4-44-2-20-4-2-2242-4220000-2-22200000000000000000000000000000004-40000000000000000000000-2200000000000
χ734-44-444-244-4-22-42-4-44-2-20-4-2-2242-4220000-2-2220000000000000000000000000000000-4400000000000000000000002-200000000000
χ744-44-44-244-2-44-42-42-4-24-2024-22-2-42-42004-4-2-222000000000000000004-4-2200000000000000000000-220000000000000000000000000
χ754-44-44-244-2-44-42-42-4-24-2024-22-2-42-4200-44-2-22200000000000000000-442-2000000000000000000002-20000000000000000000000000
χ764-44-4-244-2424-4-4-4-42-2-2402-24-4-2222-4004-4-2-22200000000000000000-224-400000000000000000000-220000000000000000000000000
χ774-44-4-244-2424-4-4-4-42-2-2402-24-4-2222-400-44-2-222000000000000000002-2-44000000000000000000002-20000000000000000000000000
χ784-44-4-2-24-2-224-42-4221-2-20-1-2-2212-122004-411-1-1000003i−3i003i−3i3i−3i0000-22-22000000000000000000001-1003i−3i000000000000000000000
χ794-44-4-2-24-2-224-42-4221-2-20-1-2-2212-122004-411-1-100000−3i3i00−3i3i−3i3i0000-22-22000000000000000000001-100−3i3i000000000000000000000
χ804-44-4-2-24-2-224-42-4221-2-20-1-2-2212-12200-4411-1-1000003i−3i003i−3i3i−3i00002-22-200000000000000000000-1100−3i3i000000000000000000000
χ814-44-4-2-24-2-224-42-4221-2-20-1-2-2212-12200-4411-1-100000−3i3i00−3i3i−3i3i00002-22-200000000000000000000-11003i−3i000000000000000000000
χ824-4-4444-2-4-4-42-2-42444-2-204222-4-2-42-24i−4i00-22-220000000000000000000004i−4i00−2i2i0000000000000000−2i2i00000000000000000000000
χ834-4-4444-2-4-4-42-2-42444-2-204222-4-2-42-2−4i4i00-22-22000000000000000000000−4i4i002i−2i00000000000000002i−2i00000000000000000000000
χ844-4-444-24-42-4-442-4-24-24-20-2-422242-4-20000-22-22000000000000000000000000000004i−4i00000000000000000000000000−2i2i000000000
χ854-4-444-24-42-4-442-4-24-24-20-2-422242-4-20000-22-2200000000000000000000000000000−4i4i000000000000000000000000002i−2i000000000
χ864-4-44-2442-42-44-4-44-2-2-240-22-4-42-22244i−4i00-22-22000000000000000000000−2i2i004i−4i0000000000000000−2i2i00000000000000000000000
χ874-4-44-2442-42-44-4-44-2-2-240-22-4-42-2224−4i4i00-22-220000000000000000000002i−2i00−4i4i00000000000000002i−2i00000000000000000000000
χ884-4-44-24-22-422-2-424-2-21-20-2-122212-1-24i−4i001-11-100000003i−3i3i−3i−3i3i00000000−2i2i00−2i2i0000000000003-300i−i00000000000000000000000
χ894-4-44-24-22-422-2-424-2-21-20-2-122212-1-24i−4i001-11-10000000−3i3i−3i3i3i−3i00000000−2i2i00−2i2i000000000000-3300i−i00000000000000000000000
χ904-4-44-24-22-422-2-424-2-21-20-2-122212-1-2−4i4i001-11-100000003i−3i3i−3i−3i3i000000002i−2i002i−2i000000000000-3300−ii00000000000000000000000
χ914-4-44-24-22-422-2-424-2-21-20-2-122212-1-2−4i4i001-11-10000000−3i3i−3i3i3i−3i000000002i−2i002i−2i0000000000003-300−ii00000000000000000000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-422282222222220000-1-1-1-1-4-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222220000-1-1-1-1444-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9488-8-8-48-44-8-4448-4-84-42-404-24-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4844-4-8-8-48442-4-40-244-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-444-444-4-4442220-2-2-22-2-222-20000-111-10006-60000-3-3330000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-444-444-4-4442220-2-2-22-2-222-20000-111-1000-66000033-3-30000000000000000000000000000000000000000000000000000000
χ988-88-88-4-48-4-8-44444-8-4-4204-42-2-4444-2000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-48-4-484-44-84-84-42-4042-44-4-24-24000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4-4-44-4444442220-222-22-2-2-2-20000-1-111000006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4-4-44-4444442220-222-22-2-2-2-20000-1-11100000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4-84-84-444-48-4-420-44-2-24-444200002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48444-884-8-4-42-4-402444-2-4-24-400002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44444-444-4-422202-2-2-2-22-2-220000-11-1100000006i−6i−3i3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44444-444-4-422202-2-2-2-22-2-220000-11-110000000−6i6i3i−3i−3i3i0000000000000000000000000000000000000000000000000000000

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