Finite Group Databasebeta

← Group #13169458

Character table — Group #13169458

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666633346666666661212443666121212121212121212121212444441212121212121212441212121212121212121212121212121212121212244441212121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-11111-1-111-1-1111-111-1-111-1-11111-11-1-11-1-1-1-111-1-1-1-1-11-1
χ311111111111111111111111111111111111111111111111111-11-11-1-1111111-1-11-111-11-11-1-111-1-11111111-11-1-1-1-111-1-1-1-1-1-11-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-11-111-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111-111111111-1-1-1-111-11111-11111111111-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-111-1-1-1-1-1-1-1-1-11-1-11-11-111-1-111-1-1-1-1-1-11-11-1-1-1-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-111-1-1-1-1-11-1-11-1-1-1-111-1-111-111
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-11-1-1111111-1-1-1-111-1-11-1-11111-1-111-1-1-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-11-1-1-11-111-1-1-1-11111-1-1-1-11-11-1-111111111-1-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-11-111-1-11-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-111-11-1-1-1-1-1-1-1111111-1-1-1111-11111-1-1-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-11-1-11-11111111-1-1-1-1-1-111-1111-11111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1111-11-1-111-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-11111-1111-11-1-11111-1-1-1-111-1-11-11-1-1111111-1-1-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1111-111-1-1-1-1-1-11111-1-1111-1-11111-1-111-1-1111-1-1
χ17222222-12-1-122-12222-1-122-1-1-12-12-1-12222-1-1-1-1-12-1-122-1-1-1-1-1-12020200-1-1-1-12200-102-1020200-1-100-1-1-1-1-1-12020000-1-1000000-100
χ18222222-12-1-122-12222-1-122-1-1-12-12-1-12222-1-1-1-1-12-1-122-1-1-1-1-1-120-20-20011-1-12200-10-21020-200110011-1-1-1-1-20-2000011000000100
χ19222222-12-1-122-12222-1-122-1-1-12-12-1-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-2020200-1-111-2-200102-10-20200-1-100-1-11111-20-2000011000000100
χ20222222-12-1-122-12222-1-122-1-1-12-12-1-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-20-20-2001111-2-20010-210-20-20011001111112020000-1-1000000-100
χ21222222-12-1-122-12222-1-1-22-1-1-12-12-1-1-2-222-1-1-1-11-211-2-2111111-2020-20011-1-1220010-2-10-20200-1-10011-1-11120-2000011000000-100
χ22222222-12-1-122-12222-1-1-22-1-1-12-12-1-1-2-222-1-1-1-11-211-2-2111111-20-20200-1-1-1-1220010210-20-2001100-1-1-1-111-2020000-1-1000000100
χ23222222-12-1-122-12222-1-1-22-1-1-12-12-1-1-2-2-2-2-1-1-1-11-211-2-21111112020-2001111-2-200-10-2-1020200-1-1001111-1-1-2020000-1-1000000100
χ24222222-12-1-122-12222-1-1-22-1-1-12-12-1-1-2-2-2-2-1-1-1-11-211-2-211111120-20200-1-111-2-200-1021020-2001100-1-111-1-120-2000011000000-100
χ2522222-12222-1-1222-1-12-12-12-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10222222220000220-1-1220-1-1-1-1-1-1-1-1-1-1000000020-1-10000-1-100000
χ2622222-12222-1-1222-1-12-12-12-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-102-22-222-2-20000-2-20-11-220-11-1-111-1-1110000000-201100001100000
χ2722222-12222-1-1222-1-12-12-12-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-22-22-2-2220000-2-201-12-201-111-1-111-1-10000000-201100001100000
χ2822222-12222-1-1222-1-12-12-12-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-2-2-2-2-2000022011-2-201111111111000000020-1-10000-1-100000
χ2922222-12222-1-1222-1-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-2-2-211111111022-2-222-2-20000-2-20112-20-1-1-1-1-1-11111000000020-1-100001100000
χ3022222-12222-1-1222-1-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-2-2-21111111102-2-22222200002201-1-2-20-11-1-11111-1-10000000-20110000-1-100000
χ3122222-12222-1-1222-1-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-2-2-2111111110-222-2-2-2-2-20000220-112201-111-1-1-1-1110000000-20110000-1-100000
χ3222222-12222-1-1222-1-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-2-2-2111111110-2-222-2-2220000-2-20-1-1-220111111-1-1-1-1000000020-1-100001100000
χ332222-122-122222-1-12-1-122-1-12-1-12-12-12222-1-1-1-12-1-1-1-1-122-1-1-1-122020-1-10022-1-1002200-1-120-1-100-1-100-1-1-1-1020020000-1-100000-10
χ342222-122-122222-1-12-1-122-1-12-1-12-12-12222-1-1-1-12-1-1-1-1-122-1-1-1-12-20-20110022-1-1002-2001-1-2011001100-1-1-1-10-200-20000110000010
χ352222-122-122222-1-12-1-122-1-12-1-12-12-122-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-22020-1-100-2-21100-2200-1120-1-100-1-10011110-200-20000110000010
χ362222-122-122222-1-12-1-122-1-12-1-12-12-122-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-20-201100-2-21100-2-20011-20110011001111020020000-1-100000-10
χ372222-122-122222-1-12-1-12-2-1-12-1-12-12-1-2-222-1-1-1-1-211111-2-21111-220-20-1-10022-1-100-2-2001120-1-1001100-1-1110-20020000-1-10000010
χ382222-122-122222-1-12-1-12-2-1-12-1-12-12-1-2-222-1-1-1-1-211111-2-21111-2-2020110022-1-100-2200-11-201100-1-100-1-1110200-200001100000-10
χ392222-122-122222-1-12-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-1-211111-2-21111220-20-1-100-2-211002-2001-120-1-100110011-1-10200-200001100000-10
χ402222-122-122222-1-12-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-1-211111-2-211112-20201100-2-211002200-1-1-201100-1-10011-1-10-20020000-1-10000010
χ412-2-22222-22-22-2-22-2-22220-2-2-22-2-222-2002i−2i2-2-220000000000000000000002i−2i2i−2i2i−2i00000000000000002i−2i00000000000002i−2i2-2000
χ422-2-22222-22-22-2-22-2-22220-2-2-22-2-222-2002i−2i2-2-220000000000000000000002i−2i2i−2i−2i2i00000000000000002i−2i0000000000000−2i2i-22000
χ432-2-22222-22-22-2-22-2-22220-2-2-22-2-222-200−2i2i2-2-22000000000000000000000−2i2i−2i2i2i−2i0000000000000000−2i2i00000000000002i−2i-22000
χ442-2-22222-22-22-2-22-2-22220-2-2-22-2-222-200−2i2i2-2-22000000000000000000000−2i2i−2i2i−2i2i0000000000000000−2i2i0000000000000−2i2i2-2000
χ4544444-2-24-2-2-2-2-244-2-2-214-2-21-2-21-21-2-2-2001111-24-2-2-2-21111110040400-2-200000000-2-2000-2001100110000000000000000000000
χ4644444-2-24-2-2-2-2-244-2-2-214-2-21-2-21-21-2-2-2001111-24-2-2-2-211111100-40-400220000000022000200-1-100-1-10000000000000000000000
χ4744444-2-24-2-2-2-2-244-2-2-21-4-2-21-2-21-21-2220011112-42222-1-1-1-1-1-10040-40022000000002-2000-2001100-1-10000000000000000000000
χ4844444-2-24-2-2-2-2-244-2-2-21-4-2-21-2-21-21-2220011112-42222-1-1-1-1-1-100-40400-2-200000000-22000200-1-100110000000000000000000000
χ494444-24-2-2-2-244-2-2-24-21-24-21-21-2-2-2-2144441111-2-211-2-2-2-21111400000000-2-2-2-200-20000-200000000001111000000000000000000
χ504444-24-2-2-2-244-2-2-24-21-24-21-21-2-2-2-2144-4-41111-2-211-2-2-2-21111-4000000002222002000020000000000-1-1-1-1000000000000000000
χ514444-24-2-2-2-244-2-2-24-21-2-4-21-21-2-2-2-21-4-444111122-1-12222-1-1-1-1-400000000-2-2-2-200200002000000000011-1-1000000000000000000
χ524444-24-2-2-2-244-2-2-24-21-2-4-21-21-2-2-2-21-4-4-4-4111122-1-12222-1-1-1-1400000000222200-20000-20000000000-1-111000000000000000000
χ534444-2-24-244-2-24-2-2-21-2-241-2-2-21-21-2-2-2-20011114-2-2-211-2-2111104040-2-2000000000-200-20-20110011000000000000000000000000
χ544444-2-24-244-2-24-2-2-21-2-241-2-2-21-21-2-2-2-20011114-2-2-211-2-211110-40-40220000000002002020-1-100-1-1000000000000000000000000
χ554444-2-24-244-2-24-2-2-21-2-2-41-2-2-21-21-2-222001111-4222-1-122-1-1-1-1040-40-2-200000000020020-201100-1-1000000000000000000000000
χ564444-2-24-244-2-24-2-2-21-2-2-41-2-2-21-21-2-222001111-4222-1-122-1-1-1-10-404022000000000-200-2020-1-10011000000000000000000000000
χ5744-4-44444-4-4-4-44-4-444440-44-4-444-4-4-4000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2422-4-4-2-4-444-2-20-4-2224-2-4220000-2-222000000000000000000023−230000000000000000000023−230000000000000000000000
χ5944-4-444-2422-4-4-2-4-444-2-20-4-2224-2-4220000-2-2220000000000000000000−232300000000000000000000−23230000000000000000000000
χ6044-4-44-244-4-4224-4-4-2-24-20242-4-2-222-423−2300-2-222000023−2323−232323−23−2300000000000000000000000000000000000000000000000000000
χ6144-4-44-244-4-4224-4-4-2-24-20242-4-2-222-4−232300-2-2220000−2323−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6244-4-44-2-242222-2-4-4-2-2-2102-2-12-212-1223−230011-1-1000023−23−33−3−333000000023−2300000000000000003-300−330000000000000000000000
χ6344-4-44-2-242222-2-4-4-2-2-2102-2-12-212-1223−230011-1-1000023−23−33−3−3330000000−23230000000000000000-33003−30000000000000000000000
χ6444-4-44-2-242222-2-4-4-2-2-2102-2-12-212-12−23230011-1-10000−23233−333−3−3000000023−230000000000000000-3300−330000000000000000000000
χ6544-4-44-2-242222-2-4-4-2-2-2102-2-12-212-12−23230011-1-10000−23233−333−3−30000000−232300000000000000003-3003−30000000000000000000000
χ6644-4-4-244-2-4-4-4-44224-2-2402-2-42-242-420000-2-22200000000000000000−2i32i30000000000000000−2i32i30000000000000000000000000000
χ6744-4-4-244-2-4-4-4-44224-2-2402-2-42-242-420000-2-222000000000000000002i3−2i300000000000000002i3−2i30000000000000000000000000000
χ6844-4-4-2-24-2-4-422422-21-2-20-1-2221-2-12223−230011-1-10000−3323−23−3−33300000−2i32i30000000000000000i3−i3003i−3i000000000000000000000000
χ6944-4-4-2-24-2-4-422422-21-2-20-1-2221-2-12223−230011-1-10000−3323−23−3−333000002i3−2i30000000000000000−i3i300−3i3i000000000000000000000000
χ7044-4-4-2-24-2-4-422422-21-2-20-1-2221-2-122−23230011-1-100003−3−232333−3−300000−2i32i30000000000000000i3−i300−3i3i000000000000000000000000
χ7144-4-4-2-24-2-4-422422-21-2-20-1-2221-2-122−23230011-1-100003−3−232333−3−3000002i3−2i30000000000000000−i3i3003i−3i000000000000000000000000
χ724-44-4444-4-44-44-4-44-444404-44-4-4-4-4-4400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-42-2-442-44-44-2-2042-22-42-42-20000-22-2200000000000000000000000000000000000000000000000000000023−23000000000
χ744-44-444-2-42-2-442-44-44-2-2042-22-42-42-20000-22-22000000000000000000000000000000000000000000000000000000−2323000000000
χ754-44-44-24-4-442-2-4-442-24-20-2-4-2-4222240000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ764-44-44-24-4-442-2-4-442-24-20-2-4-2-4222240000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ774-44-4-2442-44-44-42-2-4-2-240-22422-42-4-20000-22-220000000000000000000000000000000000000000000000000000000023−230000000
χ784-44-4-2442-44-44-42-2-4-2-240-22422-42-4-20000-22-2200000000000000000000000000000000000000000000000000000000−23230000000
χ794-4-4444-2-4-224-424-4-44-2-20-422-2-424-22004i−4i-222-2000000000000000000000−2i2i4i−4i000000000000000000−2i2i00000000000000000000
χ804-4-4444-2-4-224-424-4-44-2-20-422-2-424-2200−4i4i-222-20000000000000000000002i−2i−4i4i0000000000000000002i−2i00000000000000000000
χ814-4-444-24-44-4-22-44-42-24-202-42422-2-2-40000-222-200000000000000000000000004i−4i0000000000000000000000000000000−2i2i00000
χ824-4-444-24-44-4-22-44-42-24-202-42422-2-2-40000-222-20000000000000000000000000−4i4i00000000000000000000000000000002i−2i00000
χ834-4-44-24424-44-4-4-22-4-2-24022-4-22-4-242004i−4i-222-20000000000000000000004i−4i−2i2i000000000000000000−2i2i00000000000000000000
χ844-4-44-24424-44-4-4-22-4-2-24022-4-22-4-24200−4i4i-222-2000000000000000000000−4i4i2i−2i0000000000000000002i−2i00000000000000000000
χ854-4-44-24-22-224-42-22-4-21-202-12122-2-2-1004i−4i1-1-11003-300003-33-3000000000−2i2i−2i2i000000000000000000i−i3i−3i000000000000000000
χ864-4-44-24-22-224-42-22-4-21-202-12122-2-2-1004i−4i1-1-1100-330000-33-33000000000−2i2i−2i2i000000000000000000i−i−3i3i000000000000000000
χ874-4-44-24-22-224-42-22-4-21-202-12122-2-2-100−4i4i1-1-11003-300003-33-30000000002i−2i2i−2i000000000000000000−ii−3i3i000000000000000000
χ884-4-44-24-22-224-42-22-4-21-202-12122-2-2-100−4i4i1-1-1100-330000-33-330000000002i−2i2i−2i000000000000000000−ii3i−3i000000000000000000
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
χ9188-8-8-48-4-444-8-8-4448-42-40424-2-4-444-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-44444-444-42220-22-2-222-2-2-243−4300-1-1110000−2323−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44444-444-42220-22-2-222-2-2-2−434300-1-111000023−2323−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-84-44-44-884-4-420-44244-24-2-400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-444-4-8844-4-8-42-40-4-2-4-24444200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-884-4-84-442-4-4024-44-24-24-400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444-44-444-4422202-22-2-2-2-2-220000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-44-444-4422202-22-2-2-2-2-220000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-8-44-4448-84-4-42044-2-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4848-8-44-8-4442-4-40-244-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44-444-4442220-2-2-22-2-222-20000-111-1006-60000-33-3300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44-444-4442220-2-2-22-2-222-20000-111-100-6600003-33-300000000000000000000000000000000000000000000000000000

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