Finite Group Databasebeta

← Group #13168221

Character table — Group #13168221

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612122236661212121212121212121212124444466661212121244661212121212121212121212121212121212122244466121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111-1-1-1111111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1111-1-11-111111-1-1-1-11111-1-11-11-1-1-1-111-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-1-1-1111111-1-1-111-11111-1-111111111-11-1-1-111-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-111-11-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-11-1-1-111-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111111111-11-1-1-11-1-1-1-111-1-111-1-1-1-1-111-1-111111111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-11-1-1-1-111-1-111-1-1-1-111-1111-11111-1-1-1-1-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-111-1-11-111-1-1-1-1-1-11111-1-111-1-1111-1-111-1-1-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111-1-11-11-111-1-1-1-111-1-1111-11-1-1-1-1-1-1-1-1111111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1111111-1-111-11-11-1-11111-1-111-1-11-11-1-1-1-1-1-1-1-111-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-111-11-1-1111111-1-1-1-11111-1-1111-1-111-1-1111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-111-1-1-1-11-11111-1-111-1-11111-1-1-1111-11111-1-1-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-111-1-11-1111-11111-1-111-1-111-1-1-111-1-1111111-1-1-1-11
χ17222222-122-1-122-1222-1-1222-1-1-1-1-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12220022-1-1-1-10000-1-1-1222-1000-1-1-1-1-1-100002002000-1-1000000-100
χ18222222-122-1-122-1222-1-1222-1-1-1-1-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12-2-20022-1-1110000-1-1-1-2-221000-1-111110000-200-200011000000100
χ19222222-122-1-122-1222-1-1222-1-1-1-1-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-22200-2-211-1-1000011122-2-100011-1-1-1-10000-200-200011000000100
χ20222222-122-1-122-1222-1-1222-1-1-1-1-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-200-2-211110000111-2-2-2100011111100002002000-1-1000000-100
χ21222222-122-1-122-1222-1-1-222-1-1-1-1-1-12-2-222-1-1-1-11-21111-2-21111-22-20022-1-1-1-10000-1-112-2-2100011-1-1110000-2002000-1-1000000100
χ22222222-122-1-122-1222-1-1-222-1-1-1-1-1-12-2-222-1-1-1-11-21111-2-21111-2-220022-1-1110000-1-11-22-2-10001111-1-10000200-200011000000-100
χ23222222-122-1-122-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-1-1-1-11-21111-2-2111122-200-2-211-1-1000011-12-221000-1-1-1-1110000200-200011000000-100
χ24222222-122-1-122-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-1-1-1-11-21111-2-211112-2200-2-21111000011-1-222-1000-1-111-1-10000-2002000-1-1000000100
χ2522222-122-122-1222-1-1-122-1-1-12-122-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1022220000222222000-1-102-12-100-1-1-1-1-1-1-1-102000-1-10000-1-100000
χ2622222-122-122-1222-1-1-122-1-1-12-122-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1022-2-2000022-2-2-2-2000-1-1021-2100-1-1-1-111110-20001100001100000
χ2722222-122-122-1222-1-1-122-1-1-12-122-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2220000-2-222-2-2000110-2-12-1001111-1-1-1-10-20001100001100000
χ2822222-122-122-1222-1-1-122-1-1-12-122-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-20000-2-2-2-222000110-21-21001111111102000-1-10000-1-100000
χ2922222-122-122-1222-1-1-12-2-1-1-12-122-1-11100-1-1-1-1-2-2-2-21111111102-22-20000222222000-110-2-1-2100-1-111-1-1110-2000110000-1-100000
χ3022222-122-122-1222-1-1-12-2-1-1-12-122-1-11100-1-1-1-1-2-2-2-21111111102-2-22000022-2-2-2-2000-110-212-100-1-11111-1-102000-1-100001100000
χ3122222-122-122-1222-1-1-12-2-1-1-12-122-1-11100-1-1-1-1-2-2-2-2111111110-222-20000-2-222-2-20001-102-1-210011-1-1-1-11102000-1-100001100000
χ3222222-122-122-1222-1-1-12-2-1-1-12-122-1-11100-1-1-1-1-2-2-2-2111111110-22-220000-2-2-2-2220001-10212-10011-1-111-1-10-2000110000-1-100000
χ332222-122-12222-12-12-12-12-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-120022-1-12200-1-100-1-1200-102-12-1-10000-1-1-1-1002020000-1-100000-10
χ342222-122-12222-12-12-12-12-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-1200-2-2-1-122001100-1-1200-10-21-2-1-10000111100-20-20000110000010
χ352222-122-12222-12-12-12-12-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2002211-2-200-1-10011-200102-12110000-1-1-1-100-20-20000110000010
χ362222-122-12222-12-12-12-12-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-200-2-211-2-200110011-20010-21-21100001111002020000-1-100000-10
χ372222-122-12222-12-12-12-1-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-2111111-2002-2-1-12200-1-100-1-1-2001021-2110000-1-11100-2020000-1-10000010
χ382222-122-12222-12-12-12-1-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-2111111-200-22-1-122001100-1-1-20010-2-1211000011-1-10020-200001100000-10
χ392222-122-12222-12-12-12-1-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111112002-211-2-200-1-10011200-1021-2-1-10000-1-1110020-200001100000-10
χ402222-122-12222-12-12-12-1-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-2111111200-2211-2-200110011200-10-2-12-1-1000011-1-100-2020000-1-10000010
χ412-22-22222-2-2-22-22-2-222202-2-22-2-2-22-2002-222-2-2000000000000000002-22-200002i−2i2-2000000000000000000000000000002i−2i2i−2i000
χ422-22-22222-2-2-22-22-2-222202-2-22-2-2-22-2002-222-2-2000000000000000002-22-20000−2i2i2-200000000000000000000000000000−2i2i−2i2i000
χ432-22-22222-2-2-22-22-2-222202-2-22-2-2-22-200-2222-2-200000000000000000-22-2200002i−2i-22000000000000000000000000000002i−2i−2i2i000
χ442-22-22222-2-2-22-22-2-222202-2-22-2-2-22-200-2222-2-200000000000000000-22-220000−2i2i-2200000000000000000000000000000−2i2i2i−2i000
χ4544444-2-24-2-2-2-24-24-2-21-24-2-21-21-2-21-2-2-2001111-24-2-211-2-21111044000000-2-20000000-2-20-20000011110000000000000000000000
χ4644444-2-24-2-2-2-24-24-2-21-24-2-21-21-2-21-2-2-2001111-24-2-211-2-211110-4-4000000220000000220200000-1-1-1-10000000000000000000000
χ4744444-2-24-2-2-2-24-24-2-21-2-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-104-4000000-2-20000000-22020000011-1-10000000000000000000000
χ4844444-2-24-2-2-2-24-24-2-21-2-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-10-440000002200000002-20-200000-1-1110000000000000000000000
χ494444-24-2-24-2-24-2-2-24-2-214-2-2-21-211-2-244441111-2-211-2-2-2-2111140000-2-2-2-200000011-200-200001100000000000000000000000000
χ504444-24-2-24-2-24-2-2-24-2-214-2-2-21-211-2-244-4-41111-2-211-2-2-2-21111-400002222000000-1-120020000-1-100000000000000000000000000
χ514444-24-2-24-2-24-2-2-24-2-21-4-2-2-21-211-2-2-4-444111122-1-12222-1-1-1-1-40000-2-2-2-20000001120020000-1-100000000000000000000000000
χ524444-24-2-24-2-24-2-2-24-2-21-4-2-2-21-211-2-2-4-4-4-4111122-1-12222-1-1-1-1400002222000000-1-1-200-200001100000000000000000000000000
χ534444-2-24-2-244-2-24-2-21-2-2411-2-2-2-2-2-21-2-20011114-2-2-2-2-211111100044000000-2-2000000000-2-2-20000001111000000000000000000
χ544444-2-24-2-244-2-24-2-21-2-2411-2-2-2-2-2-21-2-20011114-2-2-2-2-2111111000-4-400000022000000000222000000-1-1-1-1000000000000000000
χ554444-2-24-2-244-2-24-2-21-2-2-411-2-2-2-2-2-2122001111-422222-1-1-1-1-1-10004-4000000-2-2000000000-22200000011-1-1000000000000000000
χ564444-2-24-2-244-2-24-2-21-2-2-411-2-2-2-2-2-2122001111-422222-1-1-1-1-1-1000-44000000220000000002-2-2000000-1-111000000000000000000
χ5744-4-4444-44-44-44-4-4-44440-444-4-4-44-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-442-2-442-4-44-2-20-44-2222-22-40000-22-2200000000000000000000000000000000000000000000000000000023−23000000000
χ5944-4-444-2-442-2-442-4-44-2-20-44-2222-22-40000-22-22000000000000000000000000000000000000000000000000000000−2323000000000
χ6044-4-44-24-4-2-4424-4-42-2-2402-2-2-42-44220000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ6144-4-44-24-4-2-4424-4-42-2-2402-2-2-42-44220000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ6244-4-4-24424-44-4-2-42-4-24-202-242-42-2-420000-22-220000000000000000000000000000000000000000000000000000000023−230000000
χ6344-4-4-24424-44-4-2-42-4-24-202-242-42-2-420000-22-2200000000000000000000000000000000000000000000000000000000−23230000000
χ644-44-444-24-4224-4-2-4-44-2-204-42-2222-2-4004-4-2-222000000000000000004-4-22000000-22000000000000000000000000000000000000
χ654-44-444-24-4224-4-2-4-44-2-204-42-2222-2-400-44-2-22200000000000000000-442-20000002-2000000000000000000000000000000000000
χ664-44-44-2442-4-4-2-44-42-2-240-22242-4-4-220000-2-22200000000000000000000000004i−4i0000000000000000000000000000000−2i2i00000
χ674-44-44-2442-4-4-2-44-42-2-240-22242-4-4-220000-2-2220000000000000000000000000−4i4i00000000000000000000000000000002i−2i00000
χ684-44-4-244-2-4-4-44242-4-24-20-22-4-2-42242004-4-2-22200000000000000000-224-4000000-22000000000000000000000000000000000000
χ694-44-4-244-2-4-4-44242-4-24-20-22-4-2-4224200-44-2-222000000000000000002-2-440000002-2000000000000000000000000000000000000
χ704-44-4-24-2-2-42242-22-4-2-210-22212-1-1-22004-411-1-1003i−3i00003i3i−3i−3i00000-22-220000001-1000000003i−3i00000000000000000000000000
χ714-44-4-24-2-2-42242-22-4-2-210-22212-1-1-22004-411-1-100−3i3i0000−3i−3i3i3i00000-22-220000001-100000000−3i3i00000000000000000000000000
χ724-44-4-24-2-2-42242-22-4-2-210-22212-1-1-2200-4411-1-1003i−3i00003i3i−3i−3i000002-22-2000000-1100000000−3i3i00000000000000000000000000
χ734-44-4-24-2-2-42242-22-4-2-210-22212-1-1-2200-4411-1-100−3i3i0000−3i−3i3i3i000002-22-2000000-11000000003i−3i00000000000000000000000000
χ744-4-44444-4-44-4-4-4-4444440-4-4-4-444-4-4400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-4-4-22-4-42444-2-20-4-422-2-22240000-222-200000000000000000000023−23000000000000000023−23000000000000000000000000
χ764-4-4444-2-4-4-22-4-42444-2-20-4-422-2-22240000-222-2000000000000000000000−23230000000000000000−2323000000000000000000000000
χ774-4-444-24-424-42-4-44-2-2-240222-4-24-42-2−2i32i300-222-20000−2i32i3−2i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ784-4-444-24-424-42-4-44-2-2-240222-4-24-42-22i3−2i300-222-200002i3−2i32i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ794-4-444-2-2-42-222-424-2-21-2022-121-22-1-2−2i32i3001-1-110000i3−i3−2i32i3i3−i3i3−i300000000023−230000000000000000−333i−3i0000000000000000000000
χ804-4-444-2-2-42-222-424-2-21-2022-121-22-1-2−2i32i3001-1-110000i3−i3−2i32i3i3−i3i3−i3000000000−232300000000000000003−3−3i3i0000000000000000000000
χ814-4-444-2-2-42-222-424-2-21-2022-121-22-1-22i3−2i3001-1-110000−i3i32i3−2i3−i3i3−i3i300000000023−230000000000000000−33−3i3i0000000000000000000000
χ824-4-444-2-2-42-222-424-2-21-2022-121-22-1-22i3−2i3001-1-110000−i3i32i3−2i3−i3i3−i3i3000000000−232300000000000000003−33i−3i0000000000000000000000
χ834-4-44-2442-44-4-42-4-24-24-2022-424-22-4-20000-222-200000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000000
χ844-4-44-2442-44-4-42-4-24-24-2022-424-22-4-20000-222-2000000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000000
χ854-4-44-2-24224-422-4-2-21-2-20-1-122-2-2221−2i32i3001-1-110000−2i32i3i3−i3i3−i3i3−i300000000000−2i32i3000000000000000000i3−i33-3000000000000000000
χ864-4-44-2-24224-422-4-2-21-2-20-1-122-2-2221−2i32i3001-1-110000−2i32i3i3−i3i3−i3i3−i3000000000002i3−2i3000000000000000000−i3i3-33000000000000000000
χ874-4-44-2-24224-422-4-2-21-2-20-1-122-2-22212i3−2i3001-1-1100002i3−2i3−i3i3−i3i3−i3i300000000000−2i32i3000000000000000000i3−i3-33000000000000000000
χ884-4-44-2-24224-422-4-2-21-2-20-1-122-2-22212i3−2i3001-1-1100002i3−2i3−i3i3−i3i3−i3i3000000000002i3−2i3000000000000000000−i3i33-3000000000000000000
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
χ9188-8-88-4-4-8-44-4484-84-42-404-424-24-4-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4484-4-8-444-8-4-4204-4-4-24-224400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-484-4-884-4-8442-4-40-22-4444-44-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-44-44442220-222-2-2-22-2-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-44-44-44442220-222-2-2-22-2-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000
χ968-88-88-4-48444-4-8-4-84-42-40-44-2-4-24424000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-44-8-8-448442-4-402-24-4444-4-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4444-44-44422202-2-22-2-2-22-20000-1-111006i−6i0000−3i−3i3i3i00000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-4444-44-44422202-2-22-2-2-22-20000-1-11100−6i6i00003i3i−3i−3i00000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-8-44-844-48-4-420444-2-42-24-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-44444-4-42220-2-2-2-222-2-22−4i34i300-111-100002i3−2i32i3−2i3−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-44444-4-42220-2-2-2-222-2-224i3−4i300-111-10000−2i32i3−2i32i3i3−i3i3−i300000000000000000000000000000000000000000000000000000

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