Finite Group Databasebeta

← Group #13169148

Character table — Group #13169148

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121224444661212121212124466612121212121212121212121212121212122244466121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111-1-11-11111-1-1-1-111111-11-1-1-1-1-1-1-1-111-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-1111-1-1111111-1-1-1-1-1-111-1111-1-111111111-11-11-111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-11111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-11-1-1-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-111111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111111111111-1-1-1-11-1-1-1-111-1-111-1-1-111-1-11111-1-11111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1111-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111-1-1-1-1-11-1-111-1-11111-1-111-1-111-1-1111-1-111-1-1-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-11111-1-1-111-1-11111-1-11-1-11-1-1-111-1-1-1-11111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-11111111-1-1-1-1111-1-111-1-1-1-1111-1-11-1-1-111-1-1-1-1-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-111-1-11111-1-1111-1-111-1-1111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1-11-1-111111111-1-1-1-111-1-1111-1-1-1-1111111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1-1-11111-11111-1-111-1-111-111-1-11111-1-111-1-1-1-11
χ17222222-12-1-12222-122-1-122-1-1-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-122200-1-1-1-12200002-1-1-10020-12-1-10000-1-1-1-120200000000-1-100-100
χ18222222-12-1-12222-122-1-122-1-1-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-220011-1-1220000-211100-20-12110000-1-1-1-1-20-2000000001100100
χ19222222-12-1-12222-122-1-122-1-1-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-122-200-1-111-2-200002-1-1-100201-2-1-100001111-20-2000000001100100
χ20222222-12-1-12222-122-1-122-1-1-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-2001111-2-20000-211100-201-2110000111120200000000-1-100-100
χ21222222-12-1-12222-122-1-1-22-1-1-1-12-12-1-2-222-1-1-1-11-21111-2-211112-2-200-1-1-1-12200002-1-1100-201-2110000-1-111-20200000000-1-100100
χ22222222-12-1-12222-122-1-1-22-1-1-1-12-12-1-2-222-1-1-1-11-21111-2-21111-22-20011-1-1220000-211-100201-2-1-10000-1-11120-2000000001100-100
χ23222222-12-1-12222-122-1-1-22-1-1-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-211112-2200-1-111-2-200002-1-1100-20-1211000011-1-120-2000000001100-100
χ24222222-12-1-12222-122-1-1-22-1-1-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-21111-222001111-2-20000-211-10020-12-1-1000011-1-1-20200000000-1-100100
χ2522222-12-1222-1222-1-1-122-1-12-12-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-1002220022-1-1-1-10000002-1022-100-1-1-1-1-1-1-1-102020-1-1000000000-10
χ2622222-12-1222-1222-1-1-122-1-12-12-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-1002-2-20022-1-111000000-210-22-1001111-1-1-1-10-20-201100000000010
χ2722222-12-1222-1222-1-1-122-1-12-12-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100-22200-2-211-1-10000002-102-2100-1-1-1-111110-20-201100000000010
χ2822222-12-1222-1222-1-1-122-1-12-12-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100-2-2-200-2-21111000000-210-2-21001111111102020-1-1000000000-10
χ2922222-12-1222-1222-1-1-12-2-1-12-12-12-1-1-2-222-1-1-1-1-21-2-21111111100-22-20022-1-1-1-1000000-2102-2100-1-111-1-111020-20-1-100000000010
χ3022222-12-1222-1222-1-1-12-2-1-12-12-12-1-1-2-222-1-1-1-1-21-2-21111111100-2-220022-1-1110000002-10-2-210011-1-1-1-1110-202011000000000-10
χ3122222-12-1222-1222-1-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110022-200-2-211-1-1000000-21022-100-1-11111-1-10-202011000000000-10
χ3222222-12-1222-1222-1-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-1-21-2-211111111002-2200-2-211110000002-10-22-10011-1-111-1-1020-20-1-100000000010
χ332222-122222-12-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1220222200002222-1-1-12-12-1-100-1-1-1-1-1-100000000200-1-1-1-10000000
χ342222-122222-12-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1220-2-2220000-2-2-2-2-1-1-121-2-1100-1-1111100000000-20011110000000
χ352222-122222-12-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-2022-2-2000022-2-2111-2-121-10011-1-1-1-100000000-20011110000000
χ362222-122222-12-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-20-2-2-2-20000-2-222111-21-2110011111100000000200-1-1-1-10000000
χ372222-122222-12-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-21111112-202-22200002222-1-1-1-21-21-10011-1-11100000000-200-1-1110000000
χ382222-122222-12-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-21111112-20-22220000-2-2-2-2-1-1-1-2-1211001111-1-10000000020011-1-10000000
χ392222-122222-12-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-2111111-2202-2-2-2000022-2-211121-2-1-100-1-1-1-1110000000020011-1-10000000
χ402222-122222-12-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-2111111-220-22-2-20000-2-2221112-12-1100-1-111-1-100000000-200-1-1110000000
χ412-2-22222-22-222-2-2-2-22220-2-2-222-2-22-2002i−2i2-2-2200000000000000000002i−2i2i−2i002i−2i00000000000000002i−2i0000000002i−2i00002-2000
χ422-2-22222-22-222-2-2-2-22220-2-2-222-2-22-2002i−2i2-2-2200000000000000000002i−2i2i−2i00−2i2i00000000000000002i−2i000000000−2i2i0000-22000
χ432-2-22222-22-222-2-2-2-22220-2-2-222-2-22-200−2i2i2-2-220000000000000000000−2i2i−2i2i002i−2i0000000000000000−2i2i0000000002i−2i0000-22000
χ442-2-22222-22-222-2-2-2-22220-2-2-222-2-22-200−2i2i2-2-220000000000000000000−2i2i−2i2i00−2i2i0000000000000000−2i2i000000000−2i2i00002-2000
χ4544444-2-2-2-2-24-244-2-2-21-24-21-21-2-2-2-2144441111-2-2-2-211-2-211110040000-2-2-2-2000000000000-2-20000001111000000000000000000
χ4644444-2-2-2-2-24-244-2-2-21-24-21-21-2-2-2-2144-4-41111-2-2-2-211-2-2111100-40000222200000000000022000000-1-1-1-1000000000000000000
χ4744444-2-2-2-2-24-244-2-2-21-2-4-21-21-2-2-2-21-4-44411112222-1-122-1-1-1-100-40000-2-2-2-20000000000002200000011-1-1000000000000000000
χ4844444-2-2-2-2-24-244-2-2-21-2-4-21-21-2-2-2-21-4-4-4-411112222-1-122-1-1-1-100400002222000000000000-2-2000000-1-111000000000000000000
χ494444-24-24-2-2-24-2-2-24-2-214-2-21-21-21-2-2-2-2001111-2411-2-2-2-2111144000-2-200000000-211-200-20001100000000000000000000000000
χ504444-24-24-2-2-24-2-2-24-2-214-2-21-21-21-2-2-2-2001111-2411-2-2-2-21111-4-400022000000002-1-12002000-1-100000000000000000000000000
χ514444-24-24-2-2-24-2-2-24-2-21-4-2-21-21-21-2-2220011112-4-1-12222-1-1-1-14-4000-2-200000000-2112002000-1-100000000000000000000000000
χ524444-24-24-2-2-24-2-2-24-2-21-4-2-21-21-21-2-2220011112-4-1-12222-1-1-1-1-4400022000000002-1-1-200-20001100000000000000000000000000
χ534444-2-24-244-2-2-2-24-21-2-241-2-2-2-21-21-2-2-20011114-2-2-2-2-211111100044000000-2-2000000-2-20-2000011110000000000000000000000
χ544444-2-24-244-2-2-2-24-21-2-241-2-2-2-21-21-2-2-20011114-2-2-2-2-2111111000-4-40000002200000022020000-1-1-1-10000000000000000000000
χ554444-2-24-244-2-2-2-24-21-2-2-41-2-2-2-21-21-222001111-422222-1-1-1-1-1-10004-4000000-2-2000000220-2000011-1-10000000000000000000000
χ564444-2-24-244-2-2-2-24-21-2-2-41-2-2-2-21-21-222001111-422222-1-1-1-1-1-1000-4400000022000000-2-2020000-1-1110000000000000000000000
χ5744-4-44444-44-4-44-4-4-4444044-4-4-4-44-4-4000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-242-2-4-44-42-44-2-204-2222-4-2-420000-2-222000000000000000000000000000000000000000000000000000000000023−2300000
χ5944-4-444-242-2-4-44-42-44-2-204-2222-4-2-420000-2-2220000000000000000000000000000000000000000000000000000000000−232300000
χ6044-4-44-24-2-44-424-4-42-2-240-2-2-42-424220000-2-2220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ6144-4-44-24-2-44-424-4-42-2-240-2-2-42-424220000-2-22200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ6244-4-4-2444-442-4-22-4-4-24-20-242-422-22-40000-2-2220000000000000000000000000000000000000000000000000000000023−230000000
χ6344-4-4-2444-442-4-22-4-4-24-20-242-422-22-40000-2-22200000000000000000000000000000000000000000000000000000000−23230000000
χ644-44-4444-4-4-4-4-4-44444440-4-44-4-44-4-4400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ654-44-444-2-422-4-4-44-244-2-20-42-22242-4-20000-22-2200000000000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ664-44-444-2-422-4-4-44-244-2-20-42-22242-4-20000-22-22000000000000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ674-44-44-242-4-4-42-444-2-2-2402242-4-2-42-20000-22-2200000000000000000000000−2i32i300000000000000−2i32i3000000000000000000000000
χ684-44-44-242-4-4-42-444-2-2-2402242-4-2-42-20000-22-22000000000000000000000002i3−2i3000000000000002i3−2i3000000000000000000000000
χ694-44-4-244-4-4-42-42-244-24-202-4-2-42-222423−2300-22-220023−230023−232323−23−2300000000000000000000000000000000000000000000000000000
χ704-44-4-244-4-4-42-42-244-24-202-4-2-42-2224−232300-22-2200−232300−2323−23−23232300000000000000000000000000000000000000000000000000000
χ714-44-4-24-2-4222-42-2-24-2-2102212-1-2-12-223−23001-11-100−330023−23−3−33300000−2i32i3000000000i3−i300000003i−3i00000000000000000000000000
χ724-44-4-24-2-4222-42-2-24-2-2102212-1-2-12-223−23001-11-100−330023−23−3−333000002i3−2i3000000000−i3i30000000−3i3i00000000000000000000000000
χ734-44-4-24-2-4222-42-2-24-2-2102212-1-2-12-2−2323001-11-1003−300−232333−3−300000−2i32i3000000000i3−i30000000−3i3i00000000000000000000000000
χ744-44-4-24-2-4222-42-2-24-2-2102212-1-2-12-2−2323001-11-1003−300−232333−3−3000002i3−2i3000000000−i3i300000003i−3i00000000000000000000000000
χ754-44-4-2-242-4-4222-24-21-2-20-12-22212-1-223−23001-11-10023−2300−33−3−33300000000000−2i32i300000000000000i3−i33i−3i0000000000000000000000
χ764-44-4-2-242-4-4222-24-21-2-20-12-22212-1-223−23001-11-10023−2300−33−3−333000000000002i3−2i300000000000000−i3i3−3i3i0000000000000000000000
χ774-44-4-2-242-4-4222-24-21-2-20-12-22212-1-2−2323001-11-100−2323003−333−3−300000000000−2i32i300000000000000i3−i3−3i3i0000000000000000000000
χ784-44-4-2-242-4-4222-24-21-2-20-12-22212-1-2−2323001-11-100−2323003−333−3−3000000000002i3−2i300000000000000−i3i33i−3i0000000000000000000000
χ794-4-4444-2-4-2244-4-42-44-2-20-422-2-2-4242004i−4i-222-20000000000000000000−2i2i4i−4i00000000000000000000−2i2i00000000000000000000
χ804-4-4444-2-4-2244-4-42-44-2-20-422-2-2-424200−4i4i-222-200000000000000000002i−2i−4i4i000000000000000000002i−2i00000000000000000000
χ814-4-444-2424-44-2-4-4-42-2-24022-4-242-4-22004i−4i-222-200000000000000000004i−4i−2i2i00000000000000000000−2i2i00000000000000000000
χ824-4-444-2424-44-2-4-4-42-2-24022-4-242-4-2200−4i4i-222-20000000000000000000−4i4i2i−2i000000000000000000002i−2i00000000000000000000
χ834-4-444-2-22-224-2-4-422-21-202-121-222-2-1004i−4i1-1-1100003-3003-33-30000000−2i2i−2i2i00000000000000000000i−i3i−3i000000000000000000
χ844-4-444-2-22-224-2-4-422-21-202-121-222-2-1004i−4i1-1-110000-3300-33-330000000−2i2i−2i2i00000000000000000000i−i−3i3i000000000000000000
χ854-4-444-2-22-224-2-4-422-21-202-121-222-2-100−4i4i1-1-1100003-3003-33-300000002i−2i2i−2i00000000000000000000−ii−3i3i000000000000000000
χ864-4-444-2-22-224-2-4-422-21-202-121-222-2-100−4i4i1-1-110000-3300-33-3300000002i−2i2i−2i00000000000000000000−ii3i−3i000000000000000000
χ874-4-44-244-44-4-2422-4-4-24-202-424-222-2-40000-222-200000000000000000000000004i−4i000000000000000000000000000−2i2i000000000
χ884-4-44-244-44-4-2422-4-4-24-202-424-222-2-40000-222-20000000000000000000000000−4i4i0000000000000000000000000002i−2i000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-44-4-848-844-42-40-424-244-44-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-484-44-8-444-8-4-420-4-4-24-24244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-4-8844-44-842-4-402-4444-2-4-24000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-444-4444222022-2-2-2-22-2-20000-1-1110000000033−33−333300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-44-444-4444222022-2-2-2-22-2-20000-1-11100000000−333333−3300000000000000000000000000000000000000000000000000000
χ968-88-88-4-4444-84-88-4-4-42-404-2-4-24-444200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444444-4-4-42220-2-22-2-22-2-2243−4300-11-1100−232300−232333−3−300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444444-4-4-42220-2-22-2-22-2-22−434300-11-110023−230023−23−3−33300000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-8-44-48444-8-4-42044-2-424-2-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4848-8-4-444-842-4-40-244-4-4-242400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44-4-444442220-2-2-222-2-22-20000-111-100006-600-33-3300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44-4-444442220-2-2-222-2-22-20000-111-10000-66003-33-300000000000000000000000000000000000000000000000000000

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