Finite Group Databasebeta

← Group #13172144

Character table — Group #13172144

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order122233366666666623336666666666636666666666666662444441212121212121212224444666612121212121212121212121212121212244666612121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-111-1-11111-1-111-1-111111-1-11-11111111-1-1-1-1-11-1-1-1-1-111-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111-1-11111-1-1-1-11111111-11-111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111-111
χ511111111111111111111111111111111111111111111111-111-111111111-1-1-1-1-1-111-1-1-1-1-111111-1-111111111-1-11-1-1-1-1-1-1111-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-11-1-11111-1-1-1-1-1-111
χ711111111111111111111111111111111111111111111111-1-11-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-11-1-1-1-1-1-1-11111-11-1-1-1-1-111-1-1-1111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-11111-11-11-1-1-1-111-1-111-1-1-11111-1-1-1-1-1-1111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-1-1-11111-1-1-111-1-111-11-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-11111-1-11111111111-11-1-1-11-1-1-1-11111-1-1-1-1-111-1-11111-1-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-11-111-1-1-1-111-1-1111-11-1-11111-1-11-11-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-111-1-111-1-1-1-1-1-111-11-1-11111-1-111-1-11-11-1-11111-1-11-1-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1111-1-1-1-111111111-1-1-1-11-1111-11111-1-1-1-111-1-1-111-1-11111-1-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1111-1-11111-1-111-1-1-111-1-111-111-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-11-11111-1-111-1-111-11111-1-1-1-1-1-111-11
χ17222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1202202002200222200002-1-1-1-1-1-1020-1-10000-1-1-1-1200-1-1-1-100000000
χ18222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-120-220-200-2-20022-2-200002-1-1-1-1110-20-1-100001111-200111100000000
χ19222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-202-202002200-2-2-2-20000-21111-1-1020110000-1-1-1-1-200111100000000
χ20222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-20-2-20-200-2-200-2-2220000-21111110-201100001111200-1-1-1-100000000
χ21222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111202-20-2002200-2-22200002-1-1-11-110-20110000-1-111-200-1-11100000000
χ22222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-1111120-2-20200-2-200-2-2-2-200002-1-1-111-102011000011-1-120011-1-100000000
χ23222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111-20220-200220022-2-20000-2111-1-110-20-1-10000-1-11120011-1-100000000
χ24222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111-20-220200-2-20022220000-2111-11-1020-1-1000011-1-1-200-1-11100000000
χ2522222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1220220-1-10022-1-1002200-12-1-120020-1-1-1-1-1-1-100000200000-1-1000-100
χ2622222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-12-202-201100-2-2-1-100-2-200-12-1-1200-201-1-1111100000-20000011000100
χ2722222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-220-220-1-100221100-2-2001-211-20020-111-1-1-1-100000-20000011000100
χ2822222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-2-20-2-201100-2-2110022001-211-200-20111111100000200000-1-1000-100
χ2922222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-11111220-2-20-1-100-2-21100-2-200-12-1-1-20020111-1-1110000020000011000-100
χ3022222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-111112-20-22011002211002200-12-1-1-200-20-11111-1-100000-200000-1-1000100
χ3122222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-11111-2202-20-1-100-2-2-1-10022001-211200201-1-1-1-11100000-200000-1-1000100
χ3222222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-11111-2-20220110022-1-100-2-2001-211200-20-1-1-111-1-10000020000011000-100
χ332222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-102202222-1-1-1-1000000220000022-1-1200-1-1-1-1-1-1-1-1002000000-1-1-1000
χ342222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-102-202-22211-1-1000000-2-200000-2-2-11200-1-1-1-1111100-2000000111000
χ352222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-10-220-22-2-2-1-111000000-2-200000221-1-2001111-1-1-1-100-2000000111000
χ362222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-10-2-20-2-2-2-211110000002200000-2-211-20011111111002000000-1-1-1000
χ372222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-111110220-2-222-1-111000000-2-2000002-2-11-200-1-111-1-11100200000011-1000
χ382222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-1111102-20-222211110000002200000-22-1-1-200-1-11111-1-100-2000000-1-11000
χ392222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-111110-2202-2-2-2-1-1-1-100000022000002-21120011-1-1-1-11100-2000000-1-11000
χ402222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-111110-2-2022-2-211-1-1000000-2-200000-221-120011-1-111-1-100200000011-1000
χ4122-2-222222-2-22-2-2-2-2022200-2-22-22-22-2-22000000002-2-20000000000000000002-22i−2i2i−2i000000000000000000000002-2002i−2i2i−2i0000
χ4222-2-222222-2-22-2-2-2-2022200-2-22-22-22-2-22000000002-2-20000000000000000002-2−2i2i−2i2i000000000000000000000002-200−2i2i−2i2i0000
χ4322-2-222222-2-22-2-2-2-2022200-2-22-22-22-2-22000000002-2-2000000000000000000-222i−2i−2i2i00000000000000000000000-22002i−2i−2i2i0000
χ4422-2-222222-2-22-2-2-2-2022200-2-22-22-22-2-22000000002-2-2000000000000000000-22−2i2i2i−2i00000000000000000000000-2200−2i2i2i−2i0000
χ4544444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-2114-2-2-2-2-2111111111400400000000-2-2000000-2-211-2000001100000000000000000000000
χ4644444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-2114-2-2-2-2-2111111111-400-4000000002200000022-1-1200000-1-100000000000000000000000
χ4744444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-211-422222-1-1111-1-1-1-1400-40000000022000000-2-211200000-1-100000000000000000000000
χ4844444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-211-422222-1-1111-1-1-1-1-400400000000-2-200000022-1-1-2000001100000000000000000000000
χ494444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-21-24-2-211-2-2111111100400400-2-2000000000000000-2-20-200000001111000000000000000
χ504444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-21-24-2-211-2-2111111100-400-4002200000000000000022020000000-1-1-1-1000000000000000
χ514444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-212-422-1-122111-1-1-1-100400-400-2-2000000000000000-2202000000011-1-1000000000000000
χ524444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-212-422-1-122111-1-1-1-100-400400220000000000000002-20-20000000-1-111000000000000000
χ534444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-21-2-211-2-2-2-21111111040040-2-200-2-2000000000000000-20-20011110000000000000000000
χ544444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-21-2-211-2-2-2-211111110-400-4022002200000000000000020200-1-1-1-10000000000000000000
χ554444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-2122-1-12222111-1-1-1-10400-40-2-20022000000000000000-2020011-1-10000000000000000000
χ564444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-2122-1-12222111-1-1-1-10-400402200-2-200000000000000020-200-1-1110000000000000000000
χ5744-4-444-24-2224-4-4-4-404-2-200-42-224-4-222-200000000-2220000000000000000004-4000000000000000000000000000-220000000000
χ5844-4-444-24-2224-4-4-4-404-2-200-42-224-4-222-200000000-222000000000000000000-440000000000000000000000000002-20000000000
χ5944-4-44-24-24-4-442-4-420-24-2002-4-22-224-42-200000000-222000000000000000000004i−4i00000000000000000000000000000−2i2i000000
χ6044-4-44-24-24-4-442-4-420-24-2002-4-22-224-42-200000000-22200000000000000000000−4i4i000000000000000000000000000002i−2i000000
χ6144-4-4-24444-4-4-2-422-40-2-2400224-4-22-22-4-200000000-22200000000000000000000004i−4i00000000000000000000000000000−2i2i0000
χ6244-4-4-24444-4-4-2-422-40-2-2400224-4-22-22-4-200000000-2220000000000000000000000−4i4i000000000000000000000000000002i−2i0000
χ634-44-4444-4-44-4-4-44-44044400-44-4-4-44-4-44400000000-44-400000000000000000000000000000000000000000000000000000000000
χ644-44-444-2-42-22-4-44-4404-2-2−2i32i3-4-222-4422-2-20000−2i32i3−2i32i32-22−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000
χ654-44-444-2-42-22-4-44-4404-2-22i3−2i3-4-222-4422-2-200002i3−2i32i3−2i32-222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000
χ664-44-44-242-44-4-424-4-20-24-20024222-2-4-4-2-2000000002-220000000000000000−2i32i30000000000000000−2i32i300000000000000000000000
χ674-44-44-242-44-4-424-4-20-24-20024222-2-4-4-2-2000000002-2200000000000000002i3−2i300000000000000002i3−2i300000000000000000000000
χ684-44-44-2-222-22-424-4-20-2-21−2i32i32-2-1-12-222110000−2i32i3i3−i3-11-1i3i3−i3−i3000000000000−2i32i3000000003-3000000i3−i300000000000000000000000
χ694-44-44-2-222-22-424-4-20-2-21−2i32i32-2-1-12-222110000−2i32i3i3−i3-11-1i3i3−i3−i30000000000002i3−2i300000000-33000000−i3i300000000000000000000000
χ704-44-44-2-222-22-424-4-20-2-212i3−2i32-2-1-12-2221100002i3−2i3−i3i3-11-1−i3−i3i3i3000000000000−2i32i300000000-33000000i3−i300000000000000000000000
χ714-44-44-2-222-22-424-4-20-2-212i3−2i32-2-1-12-2221100002i3−2i3−i3i3-11-1−i3−i3i3i30000000000002i3−2i3000000003-3000000−i3i300000000000000000000000
χ724-44-4-244-4-44-42-4-2240-2-24002-2-4-42-2224-2000000002-2200000000000023−230000000000000000000000000023−2300000000000000000
χ734-44-4-244-4-44-42-4-2240-2-24002-2-4-42-2224-2000000002-22000000000000−232300000000000000000000000000−232300000000000000000
χ744-44-4-24-2-42-222-4-2240-21-2−2i32i321222-2-1-1-210000i3−i3−2i32i3-11-1i3i3−i3−i30000000023−2300000000000000000000000000−333i−3i000000000000000
χ754-44-4-24-2-42-222-4-2240-21-2−2i32i321222-2-1-1-210000i3−i3−2i32i3-11-1i3i3−i3−i300000000−2323000000000000000000000000003−3−3i3i000000000000000
χ764-44-4-24-2-42-222-4-2240-21-22i3−2i321222-2-1-1-210000−i3i32i3−2i3-11-1−i3−i3i3i30000000023−2300000000000000000000000000−33−3i3i000000000000000
χ774-44-4-24-2-42-222-4-2240-21-22i3−2i321222-2-1-1-210000−i3i32i3−2i3-11-1−i3−i3i3i300000000−2323000000000000000000000000003−33i−3i000000000000000
χ784-4-44444-4-4-44-44-44-40444004-4-44-4-4-44-4400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-422-2-44-44-404-2-200422-2-4-42-22-20000000022-20000000000000000000000000000000000000000000000000−2i32i300000000
χ804-4-4444-2-422-2-44-44-404-2-200422-2-4-42-22-20000000022-200000000000000000000000000000000000000000000000002i3−2i300000000
χ814-4-444-242-4-44-4-2-4420-24-200-2-42-222-442-20000000022-2000000000023−2300000000000000000000000023−23000000000000000000000
χ824-4-444-242-4-44-4-2-4420-24-200-2-42-222-442-20000000022-20000000000−2323000000000000000000000000−2323000000000000000000000
χ834-4-44-244-4-4-44242-2-40-2-2400-22-44222-2-4-20000000022-20000000000000023−23000000000000000000000023−230000000000000000000
χ844-4-44-244-4-4-44242-2-40-2-2400-22-44222-2-4-20000000022-200000000000000−23230000000000000000000000−23230000000000000000000
χ854-4-44-2-242-4-442-22-2201-2-200122-2-1-12-221003-30000-1-113-33-300000023−230023−2300000000000000000000−33−330000000000000000000
χ864-4-44-2-242-4-442-22-2201-2-200122-2-1-12-221003-30000-1-113-33-3000000−232300−2323000000000000000000003−33−30000000000000000000
χ874-4-44-2-242-4-442-22-2201-2-200122-2-1-12-22100-330000-1-11-33-3300000023−2300−232300000000000000000000−333−30000000000000000000
χ884-4-44-2-242-4-442-22-2201-2-200122-2-1-12-22100-330000-1-11-33-33000000−23230023−23000000000000000000003−3−330000000000000000000
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
χ9188-8-88-4-4-4-44484-8-840-4-4200442-2-44-44-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-48-444-4-844-80-42-4004-2-44-442-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-48-8-8-4444402-4-400-24-442-2-4442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-444-44444022200-2-22-22-22-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-4-444-44444022200-2-22-22-22-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-88-844-44-402-4-400-2-444-2244-4200000000-22-200000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444-4444-44-40222−4i34i3-22-2-2-22-2-22-100002i3−2i32i3−2i31-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-4444-44-402224i3−4i3-22-2-2-22-2-22-10000−2i32i3−2i32i31-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4444-4-8-4-8840-4-4200-44-22444-4-2200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4-844-4484-4-80-42-400-4-24-444-224200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-44-440222002-2-22-2-2-22-2-1006-6000011-1-33-330000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-44-440222002-2-22-2-2-22-2-100-66000011-13-33-30000000000000000000000000000000000000000000000000000000

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