Finite Group Databasebeta

← Group #13172128

Character table — Group #13172128

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666663666666666666666224444661212121212124444446666666121212121212121212121212124441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-111-1-111-1-1-1-111-1-11111111-1111-11111-1-1-1-1-11-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-111-111111-1-111-1-1-1-111-11-111-1-111-11111-1-111111-1-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-111-1-1-1-1-11-111-1-1-11-11-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-111-111-1-111111111-1-1-1-11-11-1-1111-11-11-1-1111111-1-1111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-111-1-1-1-1-1-1111-11-1-111-1-11-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-11-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-11111-11-1-1-1-1-11111-1-111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11-11-1-1-1-111-1-1111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1111111-1-1-1-1-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1111111-1-111-1-1-1-1-11-111-1-11-11-1-1-1-11111-1-111-111-1-1-1-1111-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-11111-1-1-1-111-11-111-1-1-1-11-11-1-111-1-111-111-1-111-1-111-111-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111-11-1-11111-11-111-1-111-1-1-111-1-111-1-111-11-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-11-1-1-1-1-1-11111-1-1-1-11-11-1-111-11-11111-1-1-1-11111-111-1-1-1-1111-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-11111-1-1111111-1-1-1-1-1-1-11111-1111111-1-1-1-1-1111111-1-1-1-11-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1111-11-1-1-1-111-1-111-11
χ17222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1220220220022000022002-1-1-1-1-1-10-1-120-1-1-1-100000200000-1-1-1-10000
χ18222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-12-202-202200-2-20000-2-200-2-11-1-1110-1120-1-11100000-20000011110000
χ19222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-220-220-2-200220000-2-20021-111-1-101-1-2011-1-100000-20000011110000
χ20222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-20-2-200-2-200002200-2111111011-20111100000200000-1-1-1-10000
χ21222222-1-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111220-2-202200-2-2000022002-1-1-1-1-1-1011-20111100000-200000-1-1110000
χ22222222-1-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-111112-20-2202200220000-2-200-2-11-1-11101-1-2011-1-10000020000011-1-10000
χ23222222-1-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-2202-20-2-200-2-20000-2-20021-111-1-10-1120-1-1110000020000011-1-10000
χ24222222-1-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-2-20220-2-2002200002200-21111110-1-120-1-1-1-100000-200000-1-1110000
χ2522222-1222-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-102202200-1-1-1-122220000-10200-1-12020-100-1-1-1-1-1-1002-1-10000000-100
χ2622222-1222-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-102-202-20011-1-1-2-2-2-20000-10200-1-1-2020100-1-1111100-2110000000100
χ2722222-1222-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-220-2200-1-11122-2-2000010-2001120-20-10011-1-1-1-100-2110000000100
χ2822222-1222-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-2-20-2-2001111-2-222000010-20011-20-20100111111002-1-10000000-100
χ2922222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110220-2-200-1-111-2-2-2-20000-10200-1-120-2010011-1-111002110000000-100
χ3022222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-1111102-20-2200111122220000-10200-1-1-20-20-1001111-1-100-2-1-10000000100
χ3122222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-2202-200-1-1-1-1-2-222000010-200112020100-1-1-1-11100-2-1-10000000100
χ3222222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-2-20220011-1-122-2-2000010-20011-2020-100-1-111-1-1002110000000-100
χ332222-1222-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202202-1-12200-1-1000022020-1-100-120-12-1-100-1-1-1-120000-1-10000-1000
χ342222-1222-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-120-220-2-1-1-2-200110000-2-2020-1-100120-1-2-1-1001111-200001100001000
χ352222-1222-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-202-202112200-1-10000-2-20-201100-1-20121100-1-1-1-1-200001100001000
χ362222-1222-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-20-211-2-200110000220-2011001-201-21100111120000-1-10000-1000
χ372222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111202-20-2-1-12200110000-2-2020-1-100-1-201-21100-1-11120000110000-1000
χ382222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-2-202-1-1-2-200-1-1000022020-1-1001-2012110011-1-1-20000-1-100001000
χ392222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-20220-2112200110000220-201100-120-1-2-1-100-1-111-20000-1-100001000
χ402222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-20-220211-2-200-1-10000-2-20-201100120-12-1-10011-1-120000110000-1000
χ412-22-2222-222-2-2-2-2-22022200-22-22-22-2-2-22000000002-2-20000000000000000002i−2i2-22i−2i000000000000000000000002i−2i2i−2i2-2000000
χ422-22-2222-222-2-2-2-2-22022200-22-22-22-2-2-22000000002-2-20000000000000000002i−2i-22−2i2i000000000000000000000002i−2i−2i2i-22000000
χ432-22-2222-222-2-2-2-2-22022200-22-22-22-2-2-22000000002-2-2000000000000000000−2i2i2-2−2i2i00000000000000000000000−2i2i−2i2i2-2000000
χ442-22-2222-222-2-2-2-2-22022200-22-22-22-2-2-22000000002-2-2000000000000000000−2i2i-222i−2i00000000000000000000000−2i2i2i−2i-22000000
χ4544444-2-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110400400000-2-200000000-20-2001100-20000110000000000000000000
χ4644444-2-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110-400-400000220000000020200-1-10020000-1-10000000000000000000
χ4744444-2-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10400-4000002200000000-20-200110020000-1-10000000000000000000
χ4844444-2-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10-400400000-2-20000000020200-1-100-20000110000000000000000000
χ494444-24-2-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111400400-2-20000000000000-2011000-20-2011000000000000000000000
χ504444-24-2-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111-400-40022000000000000020-1-10002020-1-1000000000000000000000
χ514444-24-2-2-24-2-24-24-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-1400-400-2-20000000000000-20110002020-1-1000000000000000000000
χ524444-24-2-2-24-2-24-24-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-1-40040022000000000000020-1-1000-20-2011000000000000000000000
χ534444-2-244-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-2111111100400400-2-200-2-20000000000000-2000-200001111000000000000000
χ544444-2-244-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-2111111100-400-4002200220000000000000200020000-1-1-1-1000000000000000
χ554444-2-244-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-100400-400-2-200220000000000000-20002000011-1-1000000000000000
χ564444-2-244-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-100-4004002200-2-200000000000002000-20000-1-111000000000000000
χ5744-4-44444-4-4-444-4-4-40444004-44-44-4-4-4-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-2-4-4244-4-4204-2-20042-22-2-4-422-2000000002-220000000000000000000000000000000000000000000000000000023−230000
χ5944-4-444-2-2-4-4244-4-4204-2-20042-22-2-4-422-2000000002-2200000000000000000000000000000000000000000000000000000−23230000
χ6044-4-44-244-42-44-2-42-40-24-200-2-442-222-42-2000000002-2200000000000023−230000000000000000000000000023−2300000000000000000
χ6144-4-44-244-42-44-2-42-40-24-200-2-442-222-42-2000000002-22000000000000−232300000000000000000000000000−232300000000000000000
χ6244-4-4-24442-4-4-242-4-40-2-2400-22-2-44222-4-2000000002-22000000000000000023−2300000000000000000000000023−23000000000000000
χ6344-4-4-24442-4-4-242-4-40-2-2400-22-2-44222-4-2000000002-220000000000000000−2323000000000000000000000000−2323000000000000000
χ6444-4-4-2-24422-4-2-222-401-2-20012-22-2-1-1221003-30000-11-133-3-30000000023−230023−230000000000000000000000−33−33000000000000000
χ6544-4-4-2-24422-4-2-222-401-2-20012-22-2-1-1221003-30000-11-133-3-300000000−232300−232300000000000000000000003−33−3000000000000000
χ6644-4-4-2-24422-4-2-222-401-2-20012-22-2-1-122100-330000-11-1-3-3330000000023−2300−23230000000000000000000000−333−3000000000000000
χ6744-4-4-2-24422-4-2-222-401-2-20012-22-2-1-122100-330000-11-1-3-33300000000−23230023−2300000000000000000000003−3−33000000000000000
χ684-44-444-22442-4-4-4-4-204-2-200-4-22-224-422-200000000-222000000000000000000004-400000000000000000000000000000-22000000
χ694-44-444-22442-4-4-4-4-204-2-200-4-22-224-422-200000000-22200000000000000000000-44000000000000000000000000000002-2000000
χ704-44-44-24-44-2-4-42-4240-24-20024-4-22-22-42-200000000-2220000000000000000004i−4i000000000000000000000000000−2i2i0000000000
χ714-44-44-24-44-2-4-42-4240-24-20024-4-22-22-42-200000000-222000000000000000000−4i4i0000000000000000000000000002i−2i0000000000
χ724-44-4-244-4-24-42-42-440-2-24002-224-4-222-4-200000000-22200000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ734-44-4-244-4-24-42-42-440-2-24002-224-4-222-4-200000000-2220000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ744-4-44444-4-4-44-4-444-4044400-4-4-4-4-4-4444400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ754-4-4444-22-4-4-2-4-444204-2-2−2i32i3-42222-44-2-2-20000−2i32i3−2i32i322-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ764-4-4444-22-4-4-2-4-444204-2-22i3−2i3-42222-44-2-2-200002i3−2i32i3−2i322-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ774-4-444-24-4-424-424-2-40-24-2002-4-4222-24-2-20000000022-200000000000000−2i32i30000000000000000000000−2i32i30000000000000000000
χ784-4-444-24-4-424-424-2-40-24-2002-4-4222-24-2-20000000022-2000000000000002i3−2i300000000000000000000002i3−2i30000000000000000000
χ794-4-444-2-22-42-2-424-220-2-21−2i32i3222-1-12-2-2110000−2i32i3i3−i3-1-11i3−i3i3−i30000000000−2i32i300000000000003-30000000i3−i30000000000000000000
χ804-4-444-2-22-42-2-424-220-2-21−2i32i3222-1-12-2-2110000−2i32i3i3−i3-1-11i3−i3i3−i300000000002i3−2i30000000000000-330000000−i3i30000000000000000000
χ814-4-444-2-22-42-2-424-220-2-212i3−2i3222-1-12-2-21100002i3−2i3−i3i3-1-11−i3i3−i3i30000000000−2i32i30000000000000-330000000i3−i30000000000000000000
χ824-4-444-2-22-42-2-424-220-2-212i3−2i3222-1-12-2-21100002i3−2i3−i3i3-1-11−i3i3−i3i300000000002i3−2i300000000000003-30000000−i3i30000000000000000000
χ834-4-44-244-42-442-4-24-40-2-2400222-4-42-2-24-20000000022-20000000000−2i32i3000000000000000−2i32i3000000000000000000000000000000
χ844-4-44-244-42-442-4-24-40-2-2400222-4-42-2-24-20000000022-200000000002i3−2i30000000000000002i3−2i3000000000000000000000000000000
χ854-4-44-24-222-4-22-4-2420-21-2−2i32i32-1-1222-21-210000i3−i3−2i32i3-1-11i3−i3i3−i3000000−2i32i3000000000000000i3−i300000003-3000000000000000000000
χ864-4-44-24-222-4-22-4-2420-21-2−2i32i32-1-1222-21-210000i3−i3−2i32i3-1-11i3−i3i3−i30000002i3−2i3000000000000000−i3i30000000-33000000000000000000000
χ874-4-44-24-222-4-22-4-2420-21-22i3−2i32-1-1222-21-210000−i3i32i3−2i3-1-11−i3i3−i3i3000000−2i32i3000000000000000i3−i30000000-33000000000000000000000
χ884-4-44-24-222-4-22-4-2420-21-22i3−2i32-1-1222-21-210000−i3i32i3−2i3-1-11−i3i3−i3i30000002i3−2i3000000000000000−i3i300000003-3000000000000000000000
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
χ9188-8-88-4-4-4-8448-4-8440-4-4200-44-4-22444-2200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-44-84-484-840-42-400-4-224-444-24200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4444-4-44440222002-22-22-2-2-2-2-1006-600001-11-3-3330000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4444-4-44440222002-22-22-2-2-2-2-100-6600001-1133-3-30000000000000000000000000000000000000000000000000000000
χ958-88-88-4-448-44-84-84-40-4-42004-442-2-444-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-44-4844-84-8-40-42-40042-2-44-44-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-8-4-4-84444802-4-400-2-44-442-2442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-4-444444-4022200-22-22-22-2-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-44-4-444444-4022200-22-22-22-2-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-844844-4-4-802-4-400-24444-22-4-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-4-440222−4i34i3-2-2-2-2-2-2222-100002i3−2i32i3−2i311-1−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-4-4402224i3−4i3-2-2-2-2-2-2222-10000−2i32i3−2i32i311-1i3−i3i3−i30000000000000000000000000000000000000000000000000000000

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