Finite Group Databasebeta

← Group #13172141

Character table — Group #13172141

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order1222333666666666233366666666666366666666666666622444466121212121212224444666666612121212121212121212121212244666612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1111-1-11111-1-111-1-111111111-1-11-11111-1-1-1-1-11-1-1-1-1-1-1-1111-1-1-1
χ3111111111111111111111111111111111111111111111111-1111-11111-1-111-1-1-1-1111-1-111-1-1-1111111-1-11111-1-11-1-1-1-111-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-11-111-1-1-1-1-1-11-1-11111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111-11-1111-1-11111-1-111-1-1-1-1-111-1-111111-11-1-11111111-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-1-11-1-1-1-111-1-1-1-1-1-111-111-1-1111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-111-1-1-1111
χ711111111111111111111111111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-11-1-1-1-1-1-1-1111-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-1-111-1-111-111-1-111-1-11-1-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1111-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-1111-1-111-1-11111111-1-111-1-111-1-11-1-11111-1-1-1-1-1-1-1111111-1-11-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111111-1-1-1-111-1-11-1-111-1-11-11-1-1-1-111-1-1111-1111-1-1-1-111-11-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-111-1-111-11-11111-1-111-1-11-1111-1-1-1-111-111-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-111-1-111111111-111-1-111-1-111-111-1-1-1-111-1-1-1-1-1111111-1-1-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-111-1-111-1-1-1-111-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-111-1-1111111-1-1-1-111-1-1-1-1-1-1-11-111-11111-1-11111-111-1-111-1-11-11-1
χ17222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10202220022220022000002-100-1-1-1-1-10200-1-1-1-1-1-1200-1-1-1-100000000
χ18222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1020-2-2200-2-22200-2-2000002-100-1-1-1110-200-1-11111-200111100000000
χ19222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10-2022-20022-2-200-2-200000-2100111-1-1020011-1-1-1-1-200111100000000
χ20222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10-20-2-2-200-2-2-2-2002200000-2100111110-200111111200-1-1-1-100000000
χ21222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110202-2-200-2-2-2-200-2-2000002-100-1-11-11020011-1-111200-1-11100000000
χ22222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-11111020-22-20022-2-20022000002-100-1-111-10-2001111-1-1-20011-1-100000000
χ23222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110-202-2200-2-222002200000-210011-1-110200-1-1-1-111-20011-1-100000000
χ24222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110-20-22200222200-2-200000-210011-11-10-200-1-111-1-1200-1-11100000000
χ2522222-12-122222-1-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1222002-1-100-1-1220022002-12-1-1-1-1200-10-1-1-1-10000020000000-1-1-1000
χ2622222-12-122222-1-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12-2200-2-1-100112200-2-20021-2-1-111-200-10-1-11100000-20000000111000
χ2722222-12-122222-1-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-22-20021100-1-1-2-200-2-200-2-1211-1-12001011-1-100000-20000000111000
χ2822222-12-122222-1-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-200-2110011-2-2002200-21-21111-2001011110000020000000-1-1-1000
χ2922222-12-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-1111122-200-2-1-10011-2-200-2-2002-12-1-1-1-1-200101111000002000000011-1000
χ3022222-12-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-111112-2-2002-1-100-1-1-2-200220021-2-1-1112001011-1-100000-20000000-1-11000
χ3122222-12-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-22200-211001122002200-2-1211-1-1-200-10-1-11100000-20000000-1-11000
χ3222222-12-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2-220021100-1-12200-2-200-21-21111200-10-1-1-1-1000002000000011-1000
χ332222-1222-1222-122-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-120222022-1-100-1-1000022-100-1-1000222-1-1-100-1-1-1-10020000-1-1000-100
χ342222-1222-1222-122-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202-2-20221100-1-10000-2-2-100-1-1000-2-221-1-100111100-2000011000100
χ352222-1222-1222-122-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2220-2-2-1-100110000-2-21001100022-2-11100-1-1-1-100-2000011000100
χ362222-1222-1222-122-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-2-20-2-211001100002210011000-2-2-21110011110020000-1-1000-100
χ372222-1222-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-22-2022110011000022-100-1-10002-2-2-11100-1-11100-20000-1-1000100
χ382222-1222-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-2-22022-1-100110000-2-2-100-1-1000-22-21110011-1-1002000011000-100
χ392222-1222-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-2022-20-2-21100-1-10000-2-2100110002-22-1-1-100-1-111002000011000-100
χ402222-1222-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-202-220-2-2-1-100-1-100002210011000-2221-1-10011-1-100-20000-1-1000100
χ412-22-2222222-2-2-2-2-2-2022200-22-22-22-2-2-22000000002-2-20000000000000000002-22i−2i2i−2i00000000000000000000000002-22i−2i2i−2i0000
χ422-22-2222222-2-2-2-2-2-2022200-22-22-22-2-2-22000000002-2-20000000000000000002-2−2i2i−2i2i00000000000000000000000002-2−2i2i−2i2i0000
χ432-22-2222222-2-2-2-2-2-2022200-22-22-22-2-2-22000000002-2-2000000000000000000-222i−2i−2i2i0000000000000000000000000-22−2i2i2i−2i0000
χ442-22-2222222-2-2-2-2-2-2022200-22-22-22-2-2-22000000002-2-2000000000000000000-22−2i2i2i−2i0000000000000000000000000-222i−2i−2i2i0000
χ4544444-2-2-24-2-2-24-2-244-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110400040000-2-2000000000-2-20011-2000000110000000000000000000
χ4644444-2-2-24-2-2-24-2-244-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110-4000-40000220000000002200-1-12000000-1-10000000000000000000
χ4744444-2-2-24-2-2-24-2-24-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-104000-4000022000000000-2-200112000000-1-10000000000000000000
χ4844444-2-2-24-2-2-24-2-24-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10-400040000-2-20000000002200-1-1-2000000110000000000000000000
χ494444-24-24-2-2-2-2-244-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-2111111100044000-2-2000000000000000000-2-20-200001111000000000000000
χ504444-24-24-2-2-2-2-244-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-21111111000-4-40002200000000000000000022020000-1-1-1-1000000000000000
χ514444-24-24-2-2-2-2-244-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-10004-400022000000000000000000-220-2000011-1-1000000000000000
χ524444-24-24-2-2-2-2-244-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-1000-44000-2-20000000000000000002-2020000-1-111000000000000000
χ534444-2-24-2-2444-2-2-2-24-21-244-211-2-2-2-21-21-2-2-2-211-2-21111111404000-2-20000-2-2000000-2001100000-2011000000000000000000000
χ544444-2-24-2-2444-2-2-2-24-21-244-211-2-2-2-21-21-2-2-2-211-2-21111111-40-400022000022000000200-1-10000020-1-1000000000000000000000
χ554444-2-24-2-2444-2-2-2-2-4-21-2-4-4-211-2-2-2-21-212222-1-122111-1-1-1-140-4000-2-2000022000000-200110000020-1-1000000000000000000000
χ564444-2-24-2-2444-2-2-2-2-4-21-2-4-4-211-2-2-2-21-212222-1-122111-1-1-1-1-404000220000-2-2000000200-1-100000-2011000000000000000000000
χ5744-4-4444-4-4-44-4-44-44044400-4-4-4-44-444-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-42-22-44-440-24-2002-4-42-22-242-2000000002-2200000000000000000000000000000000000000000000000−2i32i30000000000
χ5944-4-444-2-4-42-22-44-440-24-2002-4-42-22-242-2000000002-22000000000000000000000000000000000000000000000002i3−2i30000000000
χ6044-4-44-242-4-44-4-4-22404-2-200-4222-2-44-22-2000000002-220000000000−2i32i3000000000000000−2i32i3000000000000000000000000000000
χ6144-4-44-242-4-44-4-4-22404-2-200-4222-2-44-22-2000000002-2200000000002i3−2i30000000000000002i3−2i3000000000000000000000000000000
χ6244-4-4-244-42-44-424-4-20-2-2400222-442-2-2-4-2000000002-220000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000
χ6344-4-4-244-42-44-424-4-20-2-2400222-442-2-2-4-2000000002-2200000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000
χ6444-4-4-2-2422-44-42-22-20-21-2002-1-12-22-212100003-300-11-133-3-3000000−2i32i30000−2i32i3000000000i3−i30000000i3−i3000000000000000000000
χ6544-4-4-2-2422-44-42-22-20-21-2002-1-12-22-212100003-300-11-133-3-30000002i3−2i300002i3−2i3000000000−i3i30000000−i3i3000000000000000000000
χ6644-4-4-2-2422-44-42-22-20-21-2002-1-12-22-21210000-3300-11-1-3-333000000−2i32i300002i3−2i3000000000i3−i30000000−i3i3000000000000000000000
χ6744-4-4-2-2422-44-42-22-20-21-2002-1-12-22-21210000-3300-11-1-3-3330000002i3−2i30000−2i32i3000000000−i3i30000000i3−i3000000000000000000000
χ684-44-444-244-222-4-4-4-40-24-20024-4-22-22-42-200000000-2220000000000000000004-400000000000000000000000000000-2200000000
χ694-44-444-244-222-4-4-4-40-24-20024-4-22-22-42-200000000-222000000000000000000-44000000000000000000000000000002-200000000
χ704-44-44-24-244-4-4-422-404-2-200-4-22-224-422-200000000-222000000000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ714-44-44-24-244-4-4-422-404-2-200-4-22-224-422-200000000-22200000000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ724-44-4-2444-24-4-42-4-420-2-24002-224-4-222-4-200000000-22200000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ734-44-4-2444-24-4-42-4-420-2-24002-224-4-222-4-200000000-2220000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ744-4-44444-4-4-4-444-44-40444004-44-4-4-4-4-44400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-4-422-24-44-40-24-2−2i32i3-2-442222-4-2-200−2i32i300−2i32i322-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ764-4-4444-2-4-422-24-44-40-24-22i3−2i3-2-442222-4-2-2002i3−2i3002i3−2i322-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ774-4-444-242-4-4-4442-2-404-2-20042-222-4-42-2-20000000022-200000000000000−2i32i30000000000000000000000−2i32i30000000000000000000
χ784-4-444-242-4-4-4442-2-404-2-20042-222-4-42-2-20000000022-2000000000000002i3−2i300000000000000000000002i3−2i30000000000000000000
χ794-4-444-2-22-422-242-2-40-2-21−2i32i3-22-2-1-12221100−2i32i300i3−i3-1-11i3−i3i3−i30000000000−2i32i300000000000003-30000000i3−i30000000000000000000
χ804-4-444-2-22-422-242-2-40-2-21−2i32i3-22-2-1-12221100−2i32i300i3−i3-1-11i3−i3i3−i300000000002i3−2i30000000000000-330000000−i3i30000000000000000000
χ814-4-444-2-22-422-242-2-40-2-212i3−2i3-22-2-1-122211002i3−2i300−i3i3-1-11−i3i3−i3i30000000000−2i32i30000000000000-330000000i3−i30000000000000000000
χ824-4-444-2-22-422-242-2-40-2-212i3−2i3-22-2-1-122211002i3−2i300−i3i3-1-11−i3i3−i3i300000000002i3−2i300000000000003-30000000−i3i30000000000000000000
χ834-4-44-244-42-4-44-2-4420-2-2400-22-2-4-42224-20000000022-200000000000023−23000000000000000000000000000023−23000000000000000
χ844-4-44-244-42-4-44-2-4420-2-2400-22-2-4-42224-20000000022-2000000000000−23230000000000000000000000000000−2323000000000000000
χ854-4-44-24-2-4222-2-2-44201-2-2−2i32i312-222-1-12-2100i3−i300−2i32i3-1-11i3−i3i3−i30000000023−23000000000000000000000000003i−3i−33000000000000000
χ864-4-44-24-2-4222-2-2-44201-2-2−2i32i312-222-1-12-2100i3−i300−2i32i3-1-11i3−i3i3−i300000000−232300000000000000000000000000−3i3i3−3000000000000000
χ874-4-44-24-2-4222-2-2-44201-2-22i3−2i312-222-1-12-2100−i3i3002i3−2i3-1-11−i3i3−i3i30000000023−2300000000000000000000000000−3i3i−33000000000000000
χ884-4-44-24-2-4222-2-2-44201-2-22i3−2i312-222-1-12-2100−i3i3002i3−2i3-1-11−i3i3−i3i300000000−2323000000000000000000000000003i−3i3−3000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-44-84-44-8-4480-4-4200444-224-4-4-2200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-844-4448-8-402-4-400-2444-4-22-44200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4444-444-44-4022200-2-2-2-22-222-2-100006-6001-11-3-3330000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4444-444-44-4022200-2-2-2-22-222-2-10000-66001-1133-3-30000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-48-444-844-80-4-42004-442-2-444-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-48-4-4444-8-8402-4-400-2-44-442-2442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-4-48-8-844440-42-40042-2-44-44-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4-4-4444444022200-22-22-22-2-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-4-4-4444444022200-22-22-22-2-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8-88-44-440-42-400-4-224444-2-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44444-4-44-440222−4i34i32-22-2-2-2-2-22-1002i3−2i3002i3−2i311-1−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44444-4-44-4402224i3−4i32-22-2-2-2-2-22-100−2i32i300−2i32i311-1i3−i3i3−i30000000000000000000000000000000000000000000000000000000

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