Finite Group Databasebeta

← Group #13169412

Character table — Group #13169412

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212124444412121212121212124412121212121212121212121212121212121212124444412121212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1111-111-1-111111111-1-1-1-11-11-1-111-1-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-1111111-1-111-11-1-1111111-1-1-1-11111-11-11-1-1-111-1-1-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-11111111111111111-111111111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-1-1-1-11-11-1-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111-11-1-111-1-1-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-11-11-1-1-11111-1-111-1-1-1-111-11111-1-11111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-111-1-11-1-11111-1-1-1-111-111-1111-1-111-1-1-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-11-1-111-1-1-111-1-11111-1-11-1-111-1-11111-1-1-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111-1-111-11-11-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1111111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-11111-1-1-1-11111-1-11-11-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-111-111-1-1111-1-111-1-1-1-1111-1-111-1-11111-1-1111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-1-1-1-1-1111-1-111-111-1-1-1-11111-1-1-111-1111-1-111-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-1111111-11-1111-1-1-1-111-1-111-1-111-11111-1-111-1-1-1-11
χ17222222-12222-1-12-122-1-122-1-12-1-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-12002200-1-122-1-1002-10-10022-1-1-1-10000-1-1-1-10202000-1-10000000-10
χ18222222-12222-1-12-122-1-122-1-12-1-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-1200-2-2001122-1-1002-10100-2-2-1-1-1-1000011110-20-200011000000010
χ19222222-12222-1-12-122-1-122-1-12-1-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-2002200-1-1-2-21100-210-1002211110000-1-1-1-10-20-200011000000010
χ20222222-12222-1-12-122-1-122-1-12-1-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-200-2-20011-2-21100-210100-2-21111000011110202000-1-10000000-10
χ21222222-12222-1-12-122-1-1-22-1-12-1-1-12-1-2-222-1-1-1-1-21-2-211111111-2002-200-1-122-1-100-2101002-211-1-10000-1-1110-202000-1-1000000010
χ22222222-12222-1-12-122-1-1-22-1-12-1-1-12-1-2-222-1-1-1-1-21-2-211111111-200-22001122-1-100-210-100-2211-1-1000011-1-1020-2000110000000-10
χ23222222-12222-1-12-122-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-1-21-2-2111111112002-200-1-1-2-211002-101002-2-1-1110000-1-111020-2000110000000-10
χ24222222-12222-1-12-122-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-1-21-2-211111111200-220011-2-211002-10-100-22-1-111000011-1-10-202000-1-1000000010
χ2522222-1222-1-122-122-12-12-12-1-12-1-1-122222-1-1-1-1-12-1-122-1-1-1-1-1-122200-1-100-1-12200-12-102200-1-1-1-1-1-1-1-1000020200-1-100000000-100
χ2622222-1222-1-122-122-12-12-12-1-12-1-1-122222-1-1-1-1-12-1-122-1-1-1-1-1-12-2-2001100-1-12200-1210-2-200-1-1-1-111110000-20-2001100000000100
χ2722222-1222-1-122-122-12-12-12-1-12-1-1-1222-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-22200-1-10011-2-2001-2-1022001111-1-1-1-10000-20-2001100000000100
χ2822222-1222-1-122-122-12-12-12-1-12-1-1-1222-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-2-2-200110011-2-2001-210-2-20011111111000020200-1-100000000-100
χ2922222-1222-1-122-122-12-1-2-12-1-12-1-1-12-2-222-1-1-1-11-211-2-2111111-22-200-1-100-1-122001-2102-20011-1-1-1-1110000-20200-1-100000000100
χ3022222-1222-1-122-122-12-1-2-12-1-12-1-1-12-2-222-1-1-1-11-211-2-2111111-2-22001100-1-122001-2-10-220011-1-111-1-1000020-2001100000000-100
χ3122222-1222-1-122-122-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-11-211-2-211111122-200-1-10011-2-200-12102-200-1-111-1-111000020-2001100000000-100
χ3222222-1222-1-122-122-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-11-211-2-21111112-2200110011-2-200-12-10-2200-1-11111-1-10000-20200-1-100000000100
χ332222-122-1-1222222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-10222222220000220022-1-1-1-10000-1-1-1-1-1-1-1-1000020000-1-1-1-100000
χ342222-122-1-1222222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1022-2-222-2-20000-2-2002-2-1-1110000-1-1-1-111110000-20000111100000
χ352222-122-1-1222222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-10-2-222-2-2220000-2-200-2211-1-100001111-1-1-1-10000-20000111100000
χ362222-122-1-1222222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-10-2-2-2-2-2-2-2-200002200-2-21111000011111111000020000-1-1-1-100000
χ372222-122-1-1222222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-2111102-22-2222200002200-2-2-11-110000-1-111-1-1110000-2000011-1-100000
χ382222-122-1-1222222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-2111102-2-2222-2-20000-2-200-22-111-10000-1-11111-1-1000020000-1-11100000
χ392222-122-1-1222222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211110-222-2-2-2220000-2-2002-21-1-11000011-1-1-1-111000020000-1-11100000
χ402222-122-1-1222222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211110-22-22-2-2-2-200002200221-11-1000011-1-111-1-10000-2000011-1-100000
χ412-22-2222-2-22-22-2-2-222220-2-2-2-2-22-222002i−2i22-2-20000000000000000000002i−2i2i−2i2-200000000002i−2i00000000000000000002-22i−2i000
χ422-22-2222-2-22-22-2-2-222220-2-2-2-2-22-222002i−2i22-2-20000000000000000000002i−2i2i−2i-2200000000002i−2i0000000000000000000-22−2i2i000
χ432-22-2222-2-22-22-2-2-222220-2-2-2-2-22-22200−2i2i22-2-2000000000000000000000−2i2i−2i2i2-20000000000−2i2i00000000000000000002-2−2i2i000
χ442-22-2222-2-22-22-2-2-222220-2-2-2-2-22-22200−2i2i22-2-2000000000000000000000−2i2i−2i2i-220000000000−2i2i0000000000000000000-222i−2i000
χ4544444-2-244-2-2-2-2-2-24-2-214-2-21-2-211-2-244441111-2-2-2-2-2-2111111400000000-2-2-2-200-2-2000000111100000000000000000000000000
χ4644444-2-244-2-2-2-2-2-24-2-214-2-21-2-211-2-244-4-41111-2-2-2-2-2-2111111-40000000022220022000000-1-1-1-100000000000000000000000000
χ4744444-2-244-2-2-2-2-2-24-2-21-4-2-21-2-211-2-2-4-4441111222222-1-1-1-1-1-1-400000000-2-2-2-20022000000-1-11100000000000000000000000000
χ4844444-2-244-2-2-2-2-2-24-2-21-4-2-21-2-211-2-2-4-4-4-41111222222-1-1-1-1-1-1400000000222200-2-200000011-1-100000000000000000000000000
χ494444-24-2-2-244-2-24-2-2-21-24-21-2-21-2-2-21-2-20011114-2-2-211-2-211110004400-2-2000000000-200-2-2000000001111000000000000000000
χ504444-24-2-2-244-2-24-2-2-21-24-21-2-21-2-2-21-2-20011114-2-2-211-2-21111000-4-400220000000002002200000000-1-1-1-1000000000000000000
χ514444-24-2-2-244-2-24-2-2-21-2-4-21-2-21-2-2-2122001111-4222-1-122-1-1-1-10004-400-2-2000000000200-220000000011-1-1000000000000000000
χ524444-24-2-2-244-2-24-2-2-21-2-4-21-2-21-2-2-2122001111-4222-1-122-1-1-1-1000-440022000000000-2002-200000000-1-111000000000000000000
χ534444-2-24-2-2-2-244-24-21-2-241-2-21-2-2-21-2-2-2001111-2411-2-2-2-2111104400-2-20000000000-20-2-200000011110000000000000000000000
χ544444-2-24-2-2-2-244-24-21-2-241-2-21-2-2-21-2-2-2001111-2411-2-2-2-211110-4-4002200000000002022000000-1-1-1-10000000000000000000000
χ554444-2-24-2-2-2-244-24-21-2-2-41-2-21-2-2-21-2220011112-4-1-12222-1-1-1-104-400-2-2000000000020-2200000011-1-10000000000000000000000
χ564444-2-24-2-2-2-244-24-21-2-2-41-2-21-2-2-21-2220011112-4-1-12222-1-1-1-10-4400220000000000-202-2000000-1-1110000000000000000000000
χ5744-4-44444-4-4-4-4-444-44440-4-4-444-44-4-400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-4-4-4224-2-44-2-20-4224-22-2-420000-222-2000000000000000000023−23000000000000000000000023−2300000000000000000000
χ5944-4-444-24-4-4-4224-2-44-2-20-4224-22-2-420000-222-20000000000000000000−23230000000000000000000000−232300000000000000000000
χ6044-4-44-244-422-4-4-24-4-24-202-42-242-22-40000-222-20000000000000000023−230000000000000000000023−23000000000000000000000000
χ6144-4-44-244-422-4-4-24-4-24-202-42-242-22-40000-222-200000000000000000−232300000000000000000000−2323000000000000000000000000
χ6244-4-4-244-22-4-4-4-4442-2-24022-4-2-2-4422−2i32i300-222-200−2i32i3−2i32i300−2i3−2i32i32i300000000000000000000000000000000000000000000000000000
χ6344-4-4-244-22-4-4-4-4442-2-24022-4-2-2-44222i3−2i300-222-2002i3−2i32i3−2i3002i32i3−2i3−2i300000000000000000000000000000000000000000000000000000
χ6444-4-4-24-2-22-4-4224-22-21-202-12-212-22-1−2i32i3001-1-1100−2i32i3i3−i300i3i3−i3−i3000000023−230000000000000000000000−333i−3i000000000000000000
χ6544-4-4-24-2-22-4-4224-22-21-202-12-212-22-1−2i32i3001-1-1100−2i32i3i3−i300i3i3−i3−i30000000−232300000000000000000000003−3−3i3i000000000000000000
χ6644-4-4-24-2-22-4-4224-22-21-202-12-212-22-12i3−2i3001-1-11002i3−2i3−i3i300−i3−i3i3i3000000023−230000000000000000000000−33−3i3i000000000000000000
χ6744-4-4-24-2-22-4-4224-22-21-202-12-212-22-12i3−2i3001-1-11002i3−2i3−i3i300−i3−i3i3i30000000−232300000000000000000000003−33i−3i000000000000000000
χ6844-4-4-2-24-2222-4-4-2421-2-20-1221-22-2-12−2i32i3001-1-1100i3−i3−2i32i300i3i3−i3−i30000023−2300000000000000000000−333i−3i0000000000000000000000
χ6944-4-4-2-24-2222-4-4-2421-2-20-1221-22-2-12−2i32i3001-1-1100i3−i3−2i32i300i3i3−i3−i300000−2323000000000000000000003−3−3i3i0000000000000000000000
χ7044-4-4-2-24-2222-4-4-2421-2-20-1221-22-2-122i3−2i3001-1-1100−i3i32i3−2i300−i3−i3i3i30000023−2300000000000000000000−33−3i3i0000000000000000000000
χ7144-4-4-2-24-2222-4-4-2421-2-20-1221-22-2-122i3−2i3001-1-1100−i3i32i3−2i300−i3−i3i3i300000−2323000000000000000000003−33i−3i0000000000000000000000
χ724-44-444-2-4-44-4-22-4244-2-20-422-42-224-2004i−4i-2-2220000000000000000000004i−4i−2i2i000000000000−2i2i00000000000000000000000000
χ734-44-444-2-4-44-4-22-4244-2-20-422-42-224-200−4i4i-2-222000000000000000000000−4i4i2i−2i0000000000002i−2i00000000000000000000000000
χ744-44-44-24-4-4-224-42-44-24-202-422-4-22-24004i−4i-2-222000000000000000000000−2i2i4i−4i000000000000−2i2i00000000000000000000000000
χ754-44-44-24-4-4-224-42-44-24-202-422-4-22-2400−4i4i-2-2220000000000000000000002i−2i−4i4i0000000000002i−2i00000000000000000000000000
χ764-44-44-2-2-4-4-22-22224-2-21022-1221-1-2-2004i−4i11-1-10000003i−3i3i−3i3i−3i000000000−2i2i−2i2i00000000003-3i−i00000000000000000000000000
χ774-44-44-2-2-4-4-22-22224-2-21022-1221-1-2-2004i−4i11-1-1000000−3i3i−3i3i−3i3i000000000−2i2i−2i2i0000000000-33i−i00000000000000000000000000
χ784-44-44-2-2-4-4-22-22224-2-21022-1221-1-2-200−4i4i11-1-10000003i−3i3i−3i3i−3i0000000002i−2i2i−2i0000000000-33−ii00000000000000000000000000
χ794-44-44-2-2-4-4-22-22224-2-21022-1221-1-2-200−4i4i11-1-1000000−3i3i−3i3i−3i3i0000000002i−2i2i−2i00000000003-3−ii00000000000000000000000000
χ804-44-4-244224-44-4-4-4-2-2-24022-4224-4-2-20000-2-22200000000000000000000000004-40000000000000000000000000000000-2200000
χ814-44-4-244224-44-4-4-4-2-2-24022-4224-4-2-20000-2-2220000000000000000000000000-4400000000000000000000000000000002-200000
χ824-4-44444-44-44-44-4-4-44440444-4-4-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-44-442-2-42-44-2-204-2-2-4222-420000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ844-4-4444-2-44-442-2-42-44-2-204-2-2-4222-420000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ854-4-444-24-442-2-442-4-4-24-20-24-22-4222-40000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ864-4-444-24-442-2-442-4-4-24-20-24-22-4222-40000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ874-4-44-2442-2-44-44-4-42-2-240-2-2422-4-4220000-22-2200000000000000000000000000000000000000000000000000000000−2i32i30000000
χ884-4-44-2442-2-44-44-4-42-2-240-2-2422-4-4220000-22-22000000000000000000000000000000000000000000000000000000002i3−2i30000000
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
χ9188-8-88-4-48-84444-4-4-8-4-42044-2-4-4-224400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-444444-4-442220-2-2-222-22-2-2−4i34i300-111-1002i3−2i32i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-444444-4-442220-2-2-222-22-2-24i3−4i300-111-100−2i32i3−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000
χ948-88-8-48-4448-8-44-84-4-42-404-244-2-44-42000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4844-448-84-8-42-4-40-244-24-442-4000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-444-44-4444-42220-2-2-2-2-22-2220000-1-1110000006i−6i−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444-44-4444-42220-2-2-2-2-22-2220000-1-111000000−6i6i3i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-884-44-444-8-4-420-4-4244-2-24400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-4-884-4-844-42-40-42-44-2444-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-44-4-884-842-4-402-4-4-2444-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44-44-44442220222-2-2-2-2-2-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44-44-44442220222-2-2-2-2-2-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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