Finite Group Databasebeta

← Group #13169410

Character table — Group #13169410

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121244444121212121212121244121212121212121212121212121212121212121224444661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-11111-1-11-11-1111-111-1-111-1-11111-11-11-1-1-111-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-11-11-1-1111111-1-1-11-1111-11-1-111-1-1111111-1-11-11-1-1-1-111-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111-111111111-1-1-1-1111111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-111-1-1-1-1-1-1-1-11-11-1-1-11-111-1-111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-111-1-1-1-1-1-1-11-11-1-1-11-1-111-1-111-1-1-1-1-11-11-1-1-111-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1111111-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-111-1-1-11-1-1-11111-1-111-1-111-1-1111-1-111-1-1-1-11-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-11-1-11-1-1-1111-1-1-1-11111-1-11-111-11111-1-1-1-1-1-1-111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-111111111-1-1-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-111-1-1-111-1-1111111-1-1-1-11
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-111-1111-1-1-11111-1-1-1-1111-111-11111-1-1-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-1-1-1-1-11-1-1111-1111-1-1-1-111-1-11111-1-1111-1-111-1-1111-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111-1-1111
χ17222222-1-122-12222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-1022222222000022-1-12200-1-1-1-1-1-1-1-1-1-1000020000-1-10000-1-100000
χ18222222-1-122-12222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-102-22-222-2-20000-2-2-112-200-11-1-111-1-1110000-200001100001100000
χ19222222-1-122-12222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-22-22-2-2220000-2-21-1-22001-111-1-111-1-10000-200001100001100000
χ20222222-1-122-12222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-2-2-2-2-200002211-2-2001111111111000020000-1-10000-1-100000
χ21222222-1-122-12222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111022-2-2-2-2-2-2000022112200-1-11111-1-1-1-10000-20000110000-1-100000
χ22222222-1-122-12222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-21111111102-2-22-2-2220000-2-21-12-200-1111-1-1-1-111000020000-1-100001100000
χ23222222-1-122-12222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-2111111110-222-222-2-20000-2-2-11-22001-1-1-11111-1-1000020000-1-100001100000
χ24222222-1-122-12222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-2111111110-2-2222222000022-1-1-2-20011-1-1-1-111110000-20000110000-1-100000
χ2522222-1222-122-12-12-12-12-12-1-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-12020200-1-122-1-100020-12-10200-1-100-1-1-1-1-1-1002020000-1-100000-10
χ2622222-1222-122-12-12-12-12-12-1-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-120-20-2001122-1-1000-2012-10-200110011-1-1-1-100-20-20000110000010
χ2722222-1222-122-12-12-12-12-12-1-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2020200-1-1-2-21100020-1-210200-1-100-1-1111100-20-20000110000010
χ2822222-1222-122-12-12-12-12-12-1-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-20-20011-2-211000-201-210-2001100111111002020000-1-100000-10
χ2922222-1222-122-12-12-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2111-2-2111111-2020-2001122-1-1000-20-1-2102001100-1-1-1-1110020-200001100000-10
χ3022222-1222-122-12-12-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2111-2-2111111-20-20200-1-122-1-1000201-210-200-1-10011-1-11100-2020000-1-10000010
χ3122222-1222-122-12-12-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-21111112020-20011-2-211000-20-12-102001100-1-111-1-100-2020000-1-10000010
χ3222222-1222-122-12-12-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-211111120-20200-1-1-2-2110002012-10-200-1-1001111-1-10020-200001100000-10
χ332222-1222-122-12-122-1-122-1-12-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-122020-1-100-1-1220020-10-1220-1-100-1-100-1-1-1-10202000-1-1000000-100
χ342222-1222-122-12-122-1-122-1-12-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-12-20-201100-1-12200-2010-12-2011001100-1-1-1-10-20-200011000000100
χ352222-1222-122-12-122-1-122-1-12-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-22020-1-10011-2-20020-101-220-1-100-1-10011110-20-200011000000100
χ362222-1222-122-12-122-1-122-1-12-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-20110011-2-200-20101-2-201100110011110202000-1-1000000-100
χ372222-1222-122-12-122-1-12-2-1-12-1-12-12-1-2-222-1-1-1-11-21111-2-21111-220-201100-1-12200-20-101-2201100-1-100-1-111020-200011000000-100
χ382222-1222-122-12-122-1-12-2-1-12-1-12-12-1-2-222-1-1-1-11-21111-2-21111-2-2020-1-100-1-1220020101-2-20-1-1001100-1-1110-202000-1-1000000100
χ392222-1222-122-12-122-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-21111220-20110011-2-200-20-10-12201100-1-10011-1-10-202000-1-1000000100
χ402222-1222-122-12-122-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-211112-2020-1-10011-2-2002010-12-20-1-100110011-1-1020-200011000000-100
χ412-22-2222-2-2-2-222-2-222220-2-2-22-2-222-2002i−2i2-2-220000000000000000000002i−2i2i−2i2-200000000000000002i−2i00000000000002-22i−2i000
χ422-22-2222-2-2-2-222-2-222220-2-2-22-2-222-2002i−2i2-2-220000000000000000000002i−2i2i−2i-2200000000000000002i−2i0000000000000-22−2i2i000
χ432-22-2222-2-2-2-222-2-222220-2-2-22-2-222-200−2i2i2-2-22000000000000000000000−2i2i−2i2i2-20000000000000000−2i2i00000000000002-2−2i2i000
χ442-22-2222-2-2-2-222-2-222220-2-2-22-2-222-200−2i2i2-2-22000000000000000000000−2i2i−2i2i-220000000000000000−2i2i0000000000000-222i−2i000
χ4544444-2-2-24-2-24-24-2-2-2-214-2-21-2-21-21-2-2-20011114-2-2-2-2-21111110040400-2-20000000-20-2000-2001100110000000000000000000000
χ4644444-2-2-24-2-24-24-2-2-2-214-2-21-2-21-21-2-2-20011114-2-2-2-2-211111100-40-400220000000202000200-1-100-1-10000000000000000000000
χ4744444-2-2-24-2-24-24-2-2-2-21-4-2-21-2-21-21-222001111-422222-1-1-1-1-1-10040-40022000000020-2000-200-1-100110000000000000000000000
χ4844444-2-2-24-2-24-24-2-2-2-21-4-2-21-2-21-21-222001111-422222-1-1-1-1-1-100-40400-2-20000000-2020002001100-1-10000000000000000000000
χ494444-24-2-2-24-2-24-24-2-21-24-21-2-21-21-2-2-2-2001111-24-2-211-2-2111104040-2-200000000-20-2000-20110011000000000000000000000000
χ504444-24-2-2-24-2-24-24-2-21-24-21-2-21-21-2-2-2-2001111-24-2-211-2-211110-40-40220000000020200020-1-100-1-1000000000000000000000000
χ514444-24-2-2-24-2-24-24-2-21-2-4-21-2-21-21-2-2220011112-422-1-122-1-1-1-1040-40220000000020-2000-20-1-10011000000000000000000000000
χ524444-24-2-2-24-2-24-24-2-21-2-4-21-2-21-21-2-2220011112-422-1-122-1-1-1-10-4040-2-200000000-202000201100-1-1000000000000000000000000
χ534444-2-244-2-24-2-2-2-241-2-241-2-21-2-2-2-2144441111-2-211-2-2-2-21111400000000-2-2-2-2000000-2-200000000001111000000000000000000
χ544444-2-244-2-24-2-2-2-241-2-241-2-21-2-2-2-2144-4-41111-2-211-2-2-2-21111-4000000002222000000220000000000-1-1-1-1000000000000000000
χ554444-2-244-2-24-2-2-2-241-2-2-41-2-21-2-2-2-21-4-444111122-1-12222-1-1-1-1-400000000-2-2-2-200000022000000000011-1-1000000000000000000
χ564444-2-244-2-24-2-2-2-241-2-2-41-2-21-2-2-2-21-4-4-4-4111122-1-12222-1-1-1-14000000002222000000-2-20000000000-1-111000000000000000000
χ5744-4-44444-4-4-4-4-444-44440-444-4-4-4-4-44000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-2-4-42-4-44424-2-20-4-2-2-4222240000-2-2220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ5944-4-444-2-2-4-42-4-44424-2-20-4-2-2-4222240000-2-22200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ6044-4-44-244-42-4-424-2-4-24-2024-22-42-42-20000-2-2220000000000000000000000000000000000000000000000000000000023−230000000
χ6144-4-44-244-42-4-424-2-4-24-2024-22-42-42-20000-2-22200000000000000000000000000000000000000000000000000000000−23230000000
χ6244-4-4-24442-4-42-4-24-4-2-2402-2422-42-4-20000-2-22200000000000000000000000000000000000000000000000000000023−23000000000
χ6344-4-4-24442-4-42-4-24-4-2-2402-2422-42-4-20000-2-222000000000000000000000000000000000000000000000000000000−2323000000000
χ644-44-444-22-4-4244-4-4-24-2-20-422422-2-2-40000-222-200000000000000000000000004-40000000000000000000000000000000-2200000
χ654-44-444-22-4-4244-4-4-24-2-20-422422-2-2-40000-222-20000000000000000000000000-4400000000000000000000000000000002-200000
χ664-44-44-24-4-42-44-2-424-24-202-42-2-424-22004i−4i-222-20000000000000000000004i−4i−2i2i000000000000000000−2i2i00000000000000000000
χ674-44-44-24-4-42-44-2-424-24-202-42-2-424-2200−4i4i-222-2000000000000000000000−4i4i2i−2i0000000000000000002i−2i00000000000000000000
χ684-44-4-244-42-4-4-242-44-2-24022-4-22-4-242004i−4i-222-2000000000000000000000−2i2i4i−4i000000000000000000−2i2i00000000000000000000
χ694-44-4-244-42-4-4-242-44-2-24022-4-22-4-24200−4i4i-222-20000000000000000000002i−2i−4i4i0000000000000000002i−2i00000000000000000000
χ704-44-4-2-24-422-4-2-22241-2-20-122122-2-2-1004i−4i1-1-11003-3000033-3-3000000000−2i2i−2i2i000000000000000000i−i3i−3i000000000000000000
χ714-44-4-2-24-422-4-2-22241-2-20-122122-2-2-1004i−4i1-1-1100-330000-3-333000000000−2i2i−2i2i000000000000000000i−i−3i3i000000000000000000
χ724-44-4-2-24-422-4-2-22241-2-20-122122-2-2-100−4i4i1-1-11003-3000033-3-30000000002i−2i2i−2i000000000000000000−ii−3i3i000000000000000000
χ734-44-4-2-24-422-4-2-22241-2-20-122122-2-2-100−4i4i1-1-1100-330000-3-3330000000002i−2i2i−2i000000000000000000−ii3i−3i000000000000000000
χ744-4-44444-4444-4-4-4-4-444404-4-4-444-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2244-2-4-4-4-424-2-20422-4-2-222-423−2300-22-22000023−2323−2323−2323−2300000000000000000000000000000000000000000000000000000
χ764-4-4444-2244-2-4-4-4-424-2-20422-4-2-222-4−232300-22-220000−2323−2323−2323−232300000000000000000000000000000000000000000000000000000
χ774-4-444-24-44-24-42-42-4-24-20-2-4224-2-4220000-22-220000000000000000000−2i32i30000000000000000−2i32i300000000000000000000000000
χ784-4-444-24-44-24-42-42-4-24-20-2-4224-2-4220000-22-2200000000000000000002i3−2i300000000000000002i3−2i300000000000000000000000000
χ794-4-444-2-224-2-2-42-422-2-210-22-12-212-1223−23001-11-1000023−23−33−33−330000000−2i32i30000000000000000i3−i3003i−3i0000000000000000000000
χ804-4-444-2-224-2-2-42-422-2-210-22-12-212-1223−23001-11-1000023−23−33−33−3300000002i3−2i30000000000000000−i3i300−3i3i0000000000000000000000
χ814-4-444-2-224-2-2-42-422-2-210-22-12-212-12−2323001-11-10000−23233−33−33−30000000−2i32i30000000000000000i3−i300−3i3i0000000000000000000000
χ824-4-444-2-224-2-2-42-422-2-210-22-12-212-12−2323001-11-10000−23233−33−33−300000002i3−2i30000000000000000−i3i3003i−3i0000000000000000000000
χ834-4-44-244-4-2442-42-4-4-2-240-22-42-242-420000-22-2200000000000000000−2i32i30000000000000000−2i32i30000000000000000000000000000
χ844-4-44-244-4-2442-42-4-4-2-240-22-42-242-420000-22-22000000000000000002i3−2i300000000000000002i3−2i30000000000000000000000000000
χ854-4-44-24-22-24-22-42-42-21-20-2-1221-2-12223−23001-11-10000−3323−23−33−3300000−2i32i30000000000000000i3−i3003i−3i000000000000000000000000
χ864-4-44-24-22-24-22-42-42-21-20-2-1221-2-12223−23001-11-10000−3323−23−33−33000002i3−2i30000000000000000−i3i300−3i3i000000000000000000000000
χ874-4-44-24-22-24-22-42-42-21-20-2-1221-2-122−2323001-11-100003−3−23233−33−300000−2i32i30000000000000000i3−i300−3i3i000000000000000000000000
χ884-4-44-24-22-24-22-42-42-21-20-2-1221-2-122−2323001-11-100003−3−23233−33−3000002i3−2i30000000000000000−i3i3003i−3i000000000000000000000000
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
χ9188-8-88-4-4-4-844-848-44-4-4204-4244-24-2-4000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-44-844-8-484-42-4042-44-24-24-4000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48844-844-4-4-82-4-40-2-4-4-244442000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-444444-4-442220-222-2-2-2-2-220000-1-1110000000033−33−333300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-444444-4-442220-222-2-2-2-2-220000-1-11100000000−333333−3300000000000000000000000000000000000000000000000000000
χ968-88-88-4-44-8448-4-84-4-4-42044-2-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-48-444-84-484-8-4-42-404-24-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-4-444-42220-2-2-22-2-222-20000-111-1006-60000-3-33300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-44444-4-444-42220-2-2-22-2-222-20000-111-100-66000033-3-300000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-8-4-484444-82-4-40244-2-4-444-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4-4-44444422202-2-2-222-2-2-243−4300-11-110000−2323−23233−33−300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4-4-44444422202-2-2-222-2-2-2−434300-11-11000023−2323−23−33−3300000000000000000000000000000000000000000000000000000

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