Finite Group Databasebeta

← Group #13172138

Character table — Group #13172138

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order1222333666666666233366666666666366666666666666624444466121212121212224444666121212121212121212121212121212121244466121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-1111111-1-111-1-1-1-1111-11-1111-1111111-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-111111-1-111-1-111-1-11111-11-11-1111-1-1-1-111111-1-1-1-111-1-1-1-11-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-111
χ511111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-11111-111-1-111111111-11-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-11-11-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11-11-11-1-1-11111-1-1-1-11-1-1-1-111-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1-1-11-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-11111-1-111-1-1111-1-1-1-1-111-1-111-1-111-1-1-111-1-11111-1-1-11-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-1111-1-111-1-1-1-1-1-1111111-11-1-11-1-1-111-1-1-1-1111-11-1-1-1-1-1-111111-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-111-1-1-1-111111111111-11-11-1-11-1-1-1-11111-1-1-1-1-11111-1-111-1-11-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-111-1-11111-111-1-111-1-11-1-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-111-1-111-1-11-11-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-11111-1-1111111-1-1-11-11-111-11111-1-1-1-111-1-1-11111-1-111-1-1-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-111-1-111-1-1-1-111-1-1-1-11-111-1111-1-11111-1-11-11-1-1-1-1-1-11111-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-111-1-111-1-1-1-1-1-111-1-1-1-1-111111-1-111-1-111-1-111-111-1-11111-1-1-111-1
χ17222222-12-122-12-12222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-122202022-1-1-1-100220000-1-1-1020-1220-1-1-1-1-1-10000002-1-10000000-100
χ18222222-12-122-12-12222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-122-20-2022-1-11100-2-20000-1-1-10-2012-20-1-11111000000-2110000000100
χ19222222-12-122-12-12222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-22020-2-211-1-100-2-20000111020-1-22011-1-1-1-1000000-2110000000100
χ20222222-12-122-12-12222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-20-20-2-21111002200001110-201-2-201111110000002-1-10000000-100
χ21222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-111112-220-202211-1-100-2-20000-1-1-10-201-22011-1-1110000002110000000-100
χ22222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-111112-2-202022111100220000-1-1-1020-1-2-201111-1-1000000-2-1-10000000100
χ23222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-11111-2220-20-2-2-1-1-1-1002200001110-201220-1-1-1-111000000-2-1-10000000100
χ24222222-12-122-12-122-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-11111-22-2020-2-2-1-11100-2-20000111020-12-20-1-111-1-10000002110000000-100
χ2522222-1222-122-12-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1220202-1-12200-1-10022002-1-1-1020-102-1-10000-1-1-1-120000-1-10000-1000
χ2622222-1222-122-12-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1220-20-2-1-122001100-2-2002-1-110-20-10-2-1-100001111-200001100001000
χ2722222-1222-122-12-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-2-2020211-2-200-1-100-2-200-211-1020102110000-1-1-1-1-200001100001000
χ2822222-1222-122-12-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-2-20-20-211-2-20011002200-21110-2010-2110000111120000-1-10000-1000
χ2922222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-111112-2020-2-1-1-2-200-1-10022002-1-110-20102110000-1-111-20000-1-100001000
χ3022222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-111112-20-202-1-1-2-2001100-2-2002-1-1-102010-211000011-1-120000110000-1000
χ3122222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-11111-22020-2112200-1-100-2-200-21110-20-102-1-10000-1-11120000110000-1000
χ3222222-1222-122-12-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-11111-220-20211220011002200-211-1020-10-2-1-1000011-1-1-20000-1-100001000
χ332222-122-122-12222-12-1-12-1-1-1-122-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1002222000022220000220002-1-120-1-100-1-1-1-1-1-1-1-10200000-1-1-1-10000
χ342222-122-122-12222-12-1-12-1-1-1-122-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1002-22-2000022-2-20000-2-2000-2-1120-1100-1-1-1-111110-20000011110000
χ352222-122-122-12222-12-1-12-1-1-1-122-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-100-22-220000-2-2220000-2-200021-1-201-1001111-1-1-1-10-20000011110000
χ362222-122-122-12222-12-1-12-1-1-1-122-1-1-1-12-122-1-1-1-122-1-1-1-1-1-1-100-2-2-2-20000-2-2-2-2000022000-211-201100111111110200000-1-1-1-10000
χ372222-122-122-12222-1-2-1-1211-1-122-1-1-1-12-1-2-21111-2-2-1-1-111110022-2-2000022220000-2-2000-211-20-1-100-1-111-1-1110200000-1-1110000
χ382222-122-122-12222-1-2-1-1211-1-122-1-1-1-12-1-2-21111-2-2-1-1-11111002-2-22000022-2-200002200021-1-20-1100-1-11111-1-10-20000011-1-10000
χ392222-122-122-12222-1-2-1-1211-1-122-1-1-1-12-1-2-21111-2-2-1-1-1111100-222-20000-2-222000022000-2-11201-10011-1-1-1-1110-20000011-1-10000
χ402222-122-122-12222-1-2-1-1211-1-122-1-1-1-12-1-2-21111-2-2-1-1-1111100-2-2220000-2-2-2-20000-2-20002-1-120110011-1-111-1-10200000-1-1110000
χ412-2-22222-2-222-2-22-2-2022200-2-22-22-22-2-22000000002-2-20000000000000000002-22i−2i2i−2i000000000000000000000002-22i−2i002i−2i0000
χ422-2-22222-2-222-2-22-2-2022200-2-22-22-22-2-22000000002-2-20000000000000000002-2−2i2i−2i2i000000000000000000000002-2−2i2i00−2i2i0000
χ432-2-22222-2-222-2-22-2-2022200-2-22-22-22-2-22000000002-2-2000000000000000000-222i−2i−2i2i00000000000000000000000-222i−2i00−2i2i0000
χ442-2-22222-2-222-2-22-2-2022200-2-22-22-22-2-22000000002-2-2000000000000000000-22−2i2i2i−2i00000000000000000000000-22−2i2i002i−2i0000
χ4544444-2-24-2-24-2-2-2-244-2-2144-2-211-2-2-2-211-2-2-2-2-2-2111111111440000-2-2-2-20000000000-2110000-2001100000000000000000000000
χ4644444-2-24-2-24-2-2-2-244-2-2144-2-211-2-2-2-211-2-2-2-2-2-2111111111-4-40000222200000000002-1-10000200-1-100000000000000000000000
χ4744444-2-24-2-24-2-2-2-24-4-2-21-4-4-2-211-2-2-2-211222222-1-1111-1-1-1-14-40000-2-2220000000000-2110000200-1-100000000000000000000000
χ4844444-2-24-2-24-2-2-2-24-4-2-21-4-4-2-211-2-2-2-211222222-1-1111-1-1-1-1-44000022-2-200000000002-1-10000-2001100000000000000000000000
χ494444-24-2-2-24-2-24-24-24-21-2-2-2-21-2-2-2-211-214-2-2-211-2-211111110040400000-2-2000000000000-20-20-200011110000000000000000000
χ504444-24-2-2-24-2-24-24-24-21-2-2-2-21-2-2-2-211-214-2-2-211-2-2111111100-40-4000002200000000000020202000-1-1-1-10000000000000000000
χ514444-24-2-2-24-2-24-24-2-4-21-222-21-2-2-2-211-21-4222-1-122111-1-1-1-10040-400000-2-20000000000002020-200011-1-10000000000000000000
χ524444-24-2-2-24-2-24-24-2-4-21-222-21-2-2-2-211-21-4222-1-122111-1-1-1-100-4040000022000000000000-20-202000-1-1110000000000000000000
χ534444-2-24-24-2-24-24-2-241-2-2-2-21-2-2-211-2-2-21-2411-2-2-2-21111111000404000000-2-2000000000-20-2000-20000001111000000000000000
χ544444-2-24-24-2-24-24-2-241-2-2-2-21-2-2-211-2-2-21-2411-2-2-2-21111111000-40-4000000220000000002020002000000-1-1-1-1000000000000000
χ554444-2-24-24-2-24-24-2-2-41-2-2221-2-2-211-2-2-212-4-1-12222111-1-1-1-100040-4000000-2-2000000000202000-200000011-1-1000000000000000
χ564444-2-24-24-2-24-24-2-2-41-2-2221-2-2-211-2-2-212-4-1-12222111-1-1-1-1000-40400000022000000000-20-20002000000-1-111000000000000000
χ5744-4-444444-4-4-44-4-4-404440044-44-4-4-4-4-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-2-4-4242-4-404-2-2004-22-2-4-4222-2000000002-220000000000000023−230000000000000000000023−23000000000000000000000
χ5944-4-444-24-2-4-4242-4-404-2-2004-22-2-4-4222-2000000002-2200000000000000−232300000000000000000000−2323000000000000000000000
χ6044-4-44-24442-4-4-2-42-40-24-200-242-222-4-42-2000000002-22000000000000000023−23000000000000000000000023−2300000000000000000
χ6144-4-44-24442-4-4-2-42-40-24-200-242-222-4-42-2000000002-220000000000000000−23230000000000000000000000−232300000000000000000
χ6244-4-4-244-24-42-44-4-420-2-24−2i32i3-2-2-442222-4-200−2i32i3−2i32i3002-22−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000
χ6344-4-4-244-24-42-44-4-420-2-242i3−2i3-2-2-442222-4-2002i3−2i32i3−2i3002-222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000
χ6444-4-4-24-2-2-2-42242-420-21-2−2i32i3-212-222-1-12100−2i32i3i3−i300-11-1i3i3−i3−i3000000000023−2300000000000000000000−333i−3i0000000000000000000
χ6544-4-4-24-2-2-2-42242-420-21-2−2i32i3-212-222-1-12100−2i32i3i3−i300-11-1i3i3−i3−i30000000000−2323000000000000000000003−3−3i3i0000000000000000000
χ6644-4-4-24-2-2-2-42242-420-21-22i3−2i3-212-222-1-121002i3−2i3−i3i300-11-1−i3−i3i3i3000000000023−2300000000000000000000−33−3i3i0000000000000000000
χ6744-4-4-24-2-2-2-42242-420-21-22i3−2i3-212-222-1-121002i3−2i3−i3i300-11-1−i3−i3i3i30000000000−2323000000000000000000003−33i−3i0000000000000000000
χ6844-4-4-2-24-2422-4-2-42201-2-2−2i32i31-22-2-1-1222100i3−i3−2i32i300-11-1i3i3−i3−i300000000000023−230000000000000000000000−333i−3i000000000000000
χ6944-4-4-2-24-2422-4-2-42201-2-2−2i32i31-22-2-1-1222100i3−i3−2i32i300-11-1i3i3−i3−i3000000000000−232300000000000000000000003−3−3i3i000000000000000
χ7044-4-4-2-24-2422-4-2-42201-2-22i3−2i31-22-2-1-1222100−i3i32i3−2i300-11-1−i3−i3i3i300000000000023−230000000000000000000000−33−3i3i000000000000000
χ7144-4-4-2-24-2422-4-2-42201-2-22i3−2i31-22-2-1-1222100−i3i32i3−2i300-11-1−i3−i3i3i3000000000000−232300000000000000000000003−33i−3i000000000000000
χ724-44-4444-4-4-4-44-4-444044400-4-4-4-4-44-444400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-42-4-4-2-424404-2-200-4222-442-2-2-20000000022-2000000000000−2i32i300000000000000000000−2i32i300000000000000000000000
χ744-44-444-2-42-4-4-2-424404-2-200-4222-442-2-2-20000000022-20000000000002i3−2i3000000000000000000002i3−2i300000000000000000000000
χ754-44-44-24-4-42-442-4-240-24-2002-4222-2-44-2-20000000022-20000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ764-44-44-24-4-42-442-4-240-24-2002-4222-2-44-2-20000000022-200000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ774-44-44-2-2-422-4-222-240-2-210022-1-12-22-2110000003-3-1-113-33-3000000−2i32i3−2i32i300000000000i3−i30000000i3−i300000000000000000000000
χ784-44-44-2-2-422-4-222-240-2-210022-1-12-22-2110000003-3-1-113-33-30000002i3−2i32i3−2i300000000000−i3i30000000−i3i300000000000000000000000
χ794-44-44-2-2-422-4-222-240-2-210022-1-12-22-211000000-33-1-11-33-33000000−2i32i32i3−2i300000000000i3−i30000000−i3i300000000000000000000000
χ804-44-44-2-2-422-4-222-240-2-210022-1-12-22-211000000-33-1-11-33-330000002i3−2i3−2i32i300000000000−i3i30000000i3−i300000000000000000000000
χ814-44-4-2442-4-424-4-44-20-2-240022-4-42-22-24-20000000022-2000000000000000000000000000000000000000000000000000−2i32i3000000
χ824-44-4-2442-4-424-4-44-20-2-240022-4-42-22-24-20000000022-20000000000000000000000000000000000000000000000000002i3−2i3000000
χ834-4-4444-2-42442-4-2-4-404-2-200-42-224-4-222-200000000-2220000000000000000004-4000000000000000000000000000-220000000000
χ844-4-4444-2-42442-4-2-4-404-2-200-42-224-4-222-200000000-222000000000000000000-440000000000000000000000000002-20000000000
χ854-4-444-24-4-4-24-4242-40-24-2002-4-22-224-42-200000000-222000000000000000000004i−4i000000000000000000000000000−2i2i00000000
χ864-4-444-24-4-4-24-4242-40-24-2002-4-22-224-42-200000000-22200000000000000000000−4i4i0000000000000000000000000002i−2i00000000
χ874-4-44-2442-44-2-4-44-420-2-2400224-4-22-22-4-200000000-22200000000000000000000004i−4i00000000000000000000000000000−2i2i0000
χ884-4-44-2442-44-2-4-44-420-2-2400224-4-22-22-4-200000000-2220000000000000000000000−4i4i000000000000000000000000000002i−2i0000
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
χ9188-8-88-4-48-44-84-444-80-4-4200-4-4-224444-2200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-4-4444-44440222−4i34i322-22-2-2-2-2-2-1002i3−2i32i3−2i3001-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-4444-444402224i3−4i322-22-2-2-2-2-2-100−2i32i3−2i32i3001-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000
χ948-88-8-48-444-84-4-848-40-42-4004-2444-4-22-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-484-84484-8-4-402-4-400-2444-224-4-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-44444-444-4-4022200-2-2-2-2-22-222-10000006-611-1-33-330000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-444-4-4022200-2-2-2-2-22-222-1000000-6611-13-33-30000000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-84-4844-44-80-4-4200442-2-44-44-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4448-44-8-4-840-42-4004-2-44-442-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-4-4-8484402-4-400-24-442-2-4442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4-444-444022200-2-22-22-22-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4-444-444022200-2-22-22-22-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000

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