Finite Group Databasebeta

← Group #13172863

Character table — Group #13172863

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666233366666666666223666666666666666444446666121212124444444466121212121212121212121212121212121212241212121212121212226124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-111-1-1-1-1-1-111-1111-111-1111111-1-1-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-111111-1-111-1-111-1-1-1-11111-1-111-1111-1-1-1-11111-11-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111-11-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-11111-1-1-1-11111-1-11-1111-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11-1-1-11111-1-1-1-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-1-11-1-1-1-1-1-111111-111-1-1-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1-111-1-111-1-1111-11-11-1-1-1-1-111-1-111-1-1-1111-1-111-1-111-11-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111111111111-1-11111-1-11-1-1-1-11-1-111-1-1-1-111-1-11111-1-111-1-1-1-11
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-1-1-111111-1-111-11-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-1-11-1-111-1-1-1-111-1-1111-1-1-11111-1-1111-1-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111-111-1-11111-1-111-1-11-1-1-11111-1-1-1-11-11
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11-111111-1-1-1-11111-1-1-1-1-1-1111111-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111-1-111-11111-111-1-11111-1-1-1-11111-1-11111-1-1-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-11-11-111111-1-111-1-111-1111-1-111-1-1-1-1-111
χ17222222-12-122-12-12222-1-1222-1-1-122-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-12022022-1-1-1-10022000000-1-10-12-10220-1-1-1-1-1-1000020-1-100000000-100
χ18222222-12-122-12-12222-1-1222-1-1-122-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-1-202-2022-1-11100-2-2000000-1-10-1-2102-20-1-111110000-201100000000100
χ19222222-12-122-12-12222-1-1222-1-1-122-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-120-220-2-211-1-100-2-200000011012-10-22011-1-1-1-10000-201100000000100
χ20222222-12-122-12-12222-1-1222-1-1-122-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-2-20-2-2111100220000001101-210-2-20111111000020-1-100000000-100
χ21222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-122-1-21-2-21111-1-1-1111120-2-2022-1-1-1-10022000000-1-101210-2-2011-1-1110000-20-1-100000000100
χ22222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-122-1-21-2-21111-1-1-11111-20-22022-1-11100-2-2000000-1-101-2-10-2201111-1-10000201100000000-100
χ23222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-1-2-2-1-21-2-21111-1-1-11111202-20-2-211-1-100-2-2000000110-12102-20-1-1-1-1110000201100000000-100
χ24222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-1-2-2-1-21-2-21111-1-1-11111-20220-2-211110022000000110-1-2-10220-1-111-1-10000-20-1-100000000100
χ2522222-1222-122-12-122-12-122-12-1-1-1-122-122-1-12-1-122-1-1-1-1-1-1-1-1-102202-1-12200-1-100220000-1-1-12002-102-1-10000-1-1-1-10200-1-10000000-10
χ2622222-1222-122-12-122-12-122-12-1-1-1-122-122-1-12-1-122-1-1-1-1-1-1-1-1-10-220-2-1-122001100-2-20000-1-11200-2-10-2-1-1000011110-20011000000010
χ2722222-1222-122-12-122-12-122-12-1-1-1-122-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-102-20211-2-200-1-100-2-2000011-1-2002102110000-1-1-1-10-20011000000010
χ2822222-1222-122-12-122-12-122-12-1-1-1-122-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-10-2-20-211-2-2001100220000111-200-210-211000011110200-1-10000000-10
χ2922222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-122-11-211-2-211-1-1-1111102-20-2-1-122001100-2-20000-1-1-1-200210-2110000-1-1110200110000000-10
χ3022222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-122-11-211-2-211-1-1-111110-2-202-1-12200-1-100220000-1-11-200-210211000011-1-10-200-1-1000000010
χ3122222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-1-2-2-11-211-2-211-1-1-111110220-211-2-200110022000011-12002-10-2-1-10000-1-1110-200-1-1000000010
χ3222222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-1-2-2-11-211-2-211-1-1-111110-220211-2-200-1-100-2-20000111200-2-102-1-1000011-1-10200110000000-10
χ332222-122-122-12222-12-1-12-1-1-1-122-1-1-1-1200-122-1-1-1-122-1-1-1-1-1-1-12202200002222000022220020-12-10-1-100-1-1-1-1-1-1-1-1000000-1-1-1-100000
χ342222-122-122-12222-12-1-12-1-1-1-122-1-1-1-1200-122-1-1-1-122-1-1-1-1-1-1-12-202-2000022-2-20000-2-2-2-200-20-1210-1100-1-1-1-11111000000111100000
χ352222-122-122-12222-12-1-12-1-1-1-122-1-1-1-1200-122-1-1-1-122-1-1-1-1-1-1-1-220-220000-2-2220000-2-2-2-200201-2-101-1001111-1-1-1-1000000111100000
χ362222-122-122-12222-12-1-12-1-1-1-122-1-1-1-1200-122-1-1-1-122-1-1-1-1-1-1-1-2-20-2-20000-2-2-2-20000222200-201-210110011111111000000-1-1-1-100000
χ372222-122-122-12222-1-2-1-1211-1-122-1-1-1-1200-1-2-21111-2-2-1-1-11111220-2-2000022-2-2000022-2-20020-1-2-101100-1-111-1-111000000-1-11100000
χ382222-122-122-12222-1-2-1-1211-1-122-1-1-1-1200-1-2-21111-2-2-1-1-111112-20-22000022220000-2-22200-20-1-2101-100-1-11111-1-100000011-1-100000
χ392222-122-122-12222-1-2-1-1211-1-122-1-1-1-1200-1-2-21111-2-2-1-1-11111-2202-20000-2-2-2-20000-2-222002012-10-110011-1-1-1-11100000011-1-100000
χ402222-122-122-12222-1-2-1-1211-1-122-1-1-1-1200-1-2-21111-2-2-1-1-11111-2-20220000-2-222000022-2-200-201210-1-10011-1-111-1-1000000-1-11100000
χ412-22-2222-2-222-2-22-2-2022200-2-22-22-22-2-2002000000002-2-2000000000000000002-22i−2i002i−2i00000000000000000000002-22i−2i002i−2i00000
χ422-22-2222-2-222-2-22-2-2022200-2-22-22-22-2-2002000000002-2-2000000000000000002-2−2i2i00−2i2i00000000000000000000002-2−2i2i00−2i2i00000
χ432-22-2222-2-222-2-22-2-2022200-2-22-22-22-2-2002000000002-2-200000000000000000-222i−2i00−2i2i0000000000000000000000-222i−2i00−2i2i00000
χ442-22-2222-2-222-2-22-2-2022200-2-22-22-22-2-2002000000002-2-200000000000000000-22−2i2i002i−2i0000000000000000000000-22−2i2i002i−2i00000
χ452-2-22222-2-2-2-22-2-222022200-2-2-2-2-22-2222-2200000000-22-20000000002-22-2000000002-2002-20000000000000000000000002-2002-2000
χ462-2-22222-2-2-2-22-2-222022200-2-2-2-2-22-2222-2200000000-22-20000000002-22-200000000-22002-2000000000000000000000000-2200-22000
χ472-2-22222-2-2-2-22-2-222022200-2-2-2-2-22-222-22200000000-22-2000000000-22-22000000002-200-220000000000000000000000002-200-22000
χ482-2-22222-2-2-2-22-2-222022200-2-2-2-2-22-222-22200000000-22-2000000000-22-2200000000-2200-22000000000000000000000000-22002-2000
χ4944444-2-24-2-24-2-2-2-244-2-2144-2-211-2-2-2-21441-2-2-2-2-2-211111111100400-2-2-2-2000000000000110-2000-2001100000000000000000000000
χ5044444-2-24-2-24-2-2-2-244-2-2144-2-211-2-2-2-21-4-41-2-2-2-2-2-211111111100-4002222000000000000-1-102000200-1-100000000000000000000000
χ5144444-2-24-2-24-2-2-2-24-4-2-21-4-4-2-211-2-2-2-21441222222-1-1111-1-1-1-100-400-2-2-2-20000000000001102000200-1-100000000000000000000000
χ5244444-2-24-2-24-2-2-2-24-4-2-21-4-4-2-211-2-2-2-21-4-41222222-1-1111-1-1-1-1004002222000000000000-1-10-2000-2001100000000000000000000000
χ534444-24-2-2-24-2-24-24-24-21-2-2-2-21-2-2-2-211-20014-2-2-211-2-21111111400400000-2-200000000000000-2-200-200011110000000000000000000
χ544444-24-2-2-24-2-24-24-24-21-2-2-2-21-2-2-2-211-20014-2-2-211-2-21111111-400-400000220000000000000022002000-1-1-1-10000000000000000000
χ554444-24-2-2-24-2-24-24-2-4-21-222-21-2-2-2-211-2001-4222-1-122111-1-1-1-1400-400000-2-200000000000000-2200200011-1-10000000000000000000
χ564444-24-2-2-24-2-24-24-2-4-21-222-21-2-2-2-211-2001-4222-1-122111-1-1-1-1-40040000022000000000000002-200-2000-1-1110000000000000000000
χ574444-2-24-24-2-24-24-2-241-2-2-2-21-2-2-211-2-2-2001-2411-2-2-2-2111111104004000000-2-20000000000-2000-200-20000001111000000000000000
χ584444-2-24-24-2-24-24-2-241-2-2-2-21-2-2-211-2-2-2001-2411-2-2-2-211111110-400-400000022000000000020002002000000-1-1-1-1000000000000000
χ594444-2-24-24-2-24-24-2-2-41-2-2221-2-2-211-2-2-20012-4-1-12222111-1-1-1-10400-4000000220000000000-2000-200200000011-1-1000000000000000
χ604444-2-24-24-2-24-24-2-2-41-2-2221-2-2-211-2-2-20012-4-1-12222111-1-1-1-10-4004000000-2-200000000002000200-2000000-1-111000000000000000
χ6144-4-444444-4-4-44-4-4-404440044-44-4-4-4-4-400400000000-4-44000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-24-2-4-4242-4-404-2-2004-22-2-4-422200-20000000022-2000000000000023−23000000000000000000000023−23000000000000000000000
χ6344-4-444-24-2-4-4242-4-404-2-2004-22-2-4-422200-20000000022-20000000000000−23230000000000000000000000−2323000000000000000000000
χ6444-4-44-24442-4-4-2-42-40-24-200-242-222-4-4200-20000000022-200000000000000023−230000000000000000000000000023−23000000000000000
χ6544-4-44-24442-4-4-2-42-40-24-200-242-222-4-4200-20000000022-2000000000000000−232300000000000000000000000000−2323000000000000000
χ6644-4-4-244-24-42-44-4-420-2-24−2i32i3-2-2-442222-400-200−2i32i3−2i32i30022-2−2i3−2i32i32i300000000000000000000000000000000000000000000000000000000
χ6744-4-4-244-24-42-44-4-420-2-242i3−2i3-2-2-442222-400-2002i3−2i32i3−2i30022-22i32i3−2i3−2i300000000000000000000000000000000000000000000000000000000
χ6844-4-4-24-2-2-2-42242-420-21-2−2i32i3-212-222-1-1200100−2i32i3i3−i300-1-11i3i3−i3−i300000000023−230000000000000000000000−333i−3i0000000000000000000
χ6944-4-4-24-2-2-2-42242-420-21-2−2i32i3-212-222-1-1200100−2i32i3i3−i300-1-11i3i3−i3−i3000000000−232300000000000000000000003−3−3i3i0000000000000000000
χ7044-4-4-24-2-2-2-42242-420-21-22i3−2i3-212-222-1-12001002i3−2i3−i3i300-1-11−i3−i3i3i300000000023−230000000000000000000000−33−3i3i0000000000000000000
χ7144-4-4-24-2-2-2-42242-420-21-22i3−2i3-212-222-1-12001002i3−2i3−i3i300-1-11−i3−i3i3i3000000000−232300000000000000000000003−33i−3i0000000000000000000
χ7244-4-4-2-24-2422-4-2-42201-2-2−2i32i31-22-2-1-122200100i3−i3−2i32i300-1-11i3i3−i3−i30000000000023−230000000000000000000000003i−3i−33000000000000000
χ7344-4-4-2-24-2422-4-2-42201-2-2−2i32i31-22-2-1-122200100i3−i3−2i32i300-1-11i3i3−i3−i300000000000−2323000000000000000000000000−3i3i3−3000000000000000
χ7444-4-4-2-24-2422-4-2-42201-2-22i3−2i31-22-2-1-122200100−i3i32i3−2i300-1-11−i3−i3i3i30000000000023−23000000000000000000000000−3i3i−33000000000000000
χ7544-4-4-2-24-2422-4-2-42201-2-22i3−2i31-22-2-1-122200100−i3i32i3−2i300-1-11−i3−i3i3i300000000000−23230000000000000000000000003i−3i3−3000000000000000
χ764-44-444-2-42442-4-2-4-404-2-200-42-224-4-22200-200000000-222000000000000000004-40000000000000000000000000000-2200000000000
χ774-44-444-2-42442-4-2-4-404-2-200-42-224-4-22200-200000000-22200000000000000000-4400000000000000000000000000002-200000000000
χ784-44-44-24-4-4-24-4242-40-24-2002-4-22-224-4200-200000000-22200000000000000000004i−4i0000000000000000000000000000−2i2i000000000
χ794-44-44-24-4-4-24-4242-40-24-2002-4-22-224-4200-200000000-2220000000000000000000−4i4i00000000000000000000000000002i−2i000000000
χ804-44-4-2442-44-2-4-44-420-2-2400224-4-22-22-400-200000000-222000000000000000000000004i−4i0000000000000000000000000000−2i2i00000
χ814-44-4-2442-44-2-4-44-420-2-2400224-4-22-22-400-200000000-22200000000000000000000000−4i4i00000000000000000000000000002i−2i00000
χ824-4-4444-2-42-4-4-2-424404-2-200-4222-442-2-24-4-2000000002-220000000004-4-22000000000000-22000000000000000000000000000000000
χ834-4-4444-2-42-4-4-2-424404-2-200-4222-442-2-2-44-2000000002-22000000000-442-20000000000002-2000000000000000000000000000000000
χ844-4-444-24-4-42-442-4-240-24-2002-4222-2-44-24-4-2000000002-22000000000-224-4000000000000-22000000000000000000000000000000000
χ854-4-444-24-4-42-442-4-240-24-2002-4222-2-44-2-44-2000000002-220000000002-2-440000000000002-2000000000000000000000000000000000
χ864-4-444-2-2-422-4-222-240-2-210022-1-12-22-214-410000003-3-11-13-33-300000-22-220000000000001-1000000003-300000000000000000000000
χ874-4-444-2-2-422-4-222-240-2-210022-1-12-22-214-41000000-33-11-1-33-3300000-22-220000000000001-100000000-3300000000000000000000000
χ884-4-444-2-2-422-4-222-240-2-210022-1-12-22-21-4410000003-3-11-13-33-3000002-22-2000000000000-1100000000-3300000000000000000000000
χ894-4-444-2-2-422-4-222-240-2-210022-1-12-22-21-441000000-33-11-1-33-33000002-22-2000000000000-11000000003-300000000000000000000000
χ904-4-44-2442-4-424-4-44-20-2-240022-4-42-22-2400-2000000002-220000000000000000000004-40000000000000000000000000000-220000000
χ914-4-44-2442-4-424-4-44-20-2-240022-4-42-22-2400-2000000002-22000000000000000000000-4400000000000000000000000000002-20000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9488-8-88-4-48-44-84-444-80-4-4200-4-4-224444-200200000000-2-22000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-4-4444-44440222−4i34i322-22-2-2-2-2-200-1002i3−2i32i3−2i30011-1−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4-4-4444-444402224i3−4i322-22-2-2-2-2-200-100−2i32i3−2i32i30011-1i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ978-88-88-4-4-84-4844-44-80-4-4200442-2-44-44-2002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ988-88-8-48-4448-44-8-4-840-42-4004-2-44-442-24002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-484-8-4-4-8484402-4-400-24-442-2-444002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-444-4-444-444022200-2-22-22-22-2-200-100000000-111−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-444-4-444-444022200-2-22-22-22-2-200-100000000-1113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-444-84-4-848-40-42-4004-2444-4-22-400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-484-84484-8-4-402-4-400-2444-224-4-400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44444-444-4-4022200-2-2-2-2-22-22200-10000006-61-11-33-3300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44444-444-4-4022200-2-2-2-2-22-22200-1000000-661-113-33-300000000000000000000000000000000000000000000000000000000

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