Finite Group Databasebeta

← Group #13168308

Character table — Group #13168308

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612122236661212121212121212121212124444466661212121244661212121212121212121212121212121212124444412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111-111-1-1111111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-1-1111111-1-111-1-11111-11-1-11111-1-1-1-11111-11-1-11-1-1-1-111-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-1-1-1111111-1-1-1-1111111-1-111111111-1-11-1-111-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1-11-1-11-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111111-1-11-1-1-111-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-1-1111111-1-111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-1-111-1-11-1-111-1-1-1-1111-11-11-1-111-1-111-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-111-1-11-1-111-1-1-1-1-11111-1-1-1111-1-1-1-1-11111-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111-1-111-11-11-1-1-1-111-1-111-1-1-11111-1-1-1-1-1-11111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1111111-1-111-1-11-11-11111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-111-111-1-111111-1-1-1-111-1111-1-1-1-1-11111111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-111-1-1-1-1111-1-111-111-1-11111-1-11-11-11-1-111-1-11111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-111-1-11111-11-1111-1-111-1-11111-1-1-1111111-1-1-1-1-1-11
χ17222222-12-1222-12-122-1-122-1-12-1-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-12002222-1-100-1-100-1-12-10-10022-1-10000-1-1-1-1020020000-1-100000-10
χ18222222-12-1222-12-122-1-122-1-12-1-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-1200-2-222-1-1001100-1-12-10100-2-2-1-1000011110-200-20000110000010
χ19222222-12-1222-12-122-1-122-1-12-1-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20022-2-21100-1-10011-210-10022110000-1-1-1-10-200-20000110000010
χ20222222-12-1222-12-122-1-122-1-12-1-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-200-2-2-2-21100110011-210100-2-21100001111020020000-1-100000-10
χ21222222-12-1222-12-122-1-1-22-1-12-1-1-12-1-2-222-1-1-1-1-21-2-211111111-2002-222-1-100-1-100-1-1-2101002-2110000-1-1110200-20000-1-10000010
χ22222222-12-1222-12-122-1-1-22-1-12-1-1-12-1-2-222-1-1-1-1-21-2-211111111-200-2222-1-1001100-1-1-210-100-2211000011-1-10-200200001100000-10
χ23222222-12-1222-12-122-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-1-21-2-2111111112002-2-2-21100-1-100112-101002-2-1-10000-1-1110-200200001100000-10
χ24222222-12-1222-12-122-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-1-21-2-211111111200-22-2-211001100112-10-100-22-1-1000011-1-10200-20000-1-10000010
χ2522222-12-1222-12-122-12-12-12-1-12-1-1-122222-1-1-1-1-12-1-122-1-1-1-1-1-122200-1-122-1-10000-1-1-12-102200-1-1-1-1-1-100002002000-1-1000000-100
χ2622222-12-1222-12-122-12-12-12-1-12-1-1-122222-1-1-1-1-12-1-122-1-1-1-1-1-12-2-200-1-122110000-1-1-1210-2-200-1-111110000-200-200011000000100
χ2722222-12-1222-12-122-12-12-12-1-12-1-1-1222-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-2220011-2-2-1-10000111-2-10220011-1-1-1-10000-200-200011000000100
χ2822222-12-1222-12-122-12-12-12-1-12-1-1-1222-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-2-2-20011-2-2110000111-210-2-20011111100002002000-1-1000000-100
χ2922222-12-1222-12-122-12-1-2-12-1-12-1-1-12-2-222-1-1-1-11-211-2-2111111-22-200-1-122-1-10000-1-11-2102-20011-1-1110000200-2000-1-1000000100
χ3022222-12-1222-12-122-12-1-2-12-1-12-1-1-12-2-222-1-1-1-11-211-2-2111111-2-2200-1-122110000-1-11-2-10-22001111-1-10000-200200011000000-100
χ3122222-12-1222-12-122-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-11-211-2-211111122-20011-2-2-1-1000011-12102-200-1-1-1-1110000-200200011000000-100
χ3222222-12-1222-12-122-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-11-211-2-21111112-220011-2-211000011-12-10-2200-1-111-1-10000200-2000-1-1000000100
χ332222-12222-1-12222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1022220000222222000022-1-1-1-100-1-1-1-1-1-1-1-100200-1-10000-1-100000
χ342222-12222-1-12222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1022-2-2000022-2-2-2-200002-2-1-11100-1-1-1-1111100-2001100001100000
χ352222-12222-1-12222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-10-2-2220000-2-222-2-20000-2211-1-1001111-1-1-1-100-2001100001100000
χ362222-12222-1-12222-1-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-10-2-2-2-20000-2-2-2-2220000-2-21111001111111100200-1-10000-1-100000
χ372222-12222-1-12222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-2111102-22-200002222220000-2-2-11-1100-1-111-1-11100-200-1-100001100000
χ382222-12222-1-12222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-2111102-2-22000022-2-2-2-20000-22-111-100-1-11111-1-100200110000-1-100000
χ392222-12222-1-12222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211110-222-20000-2-222-2-200002-21-1-110011-1-1-1-11100200110000-1-100000
χ402222-12222-1-12222-1-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211110-22-220000-2-2-2-2220000221-11-10011-1-111-1-100-200-1-100001100000
χ4122-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-2002-222-2-2000000000000000002-22-200002-22-2000000000000000000000002-20000002-2000
χ4222-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-2002-222-2-2000000000000000002-22-20000-222-200000000000000000000000-22000000-22000
χ4322-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-200-2222-2-200000000000000000-22-2200002-2-22000000000000000000000002-2000000-22000
χ4422-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-200-2222-2-200000000000000000-22-220000-22-2200000000000000000000000-220000002-2000
χ4544444-2-2-2-244-2-2-2-24-2-214-2-21-2-211-2-244441111-2-2-2-2-2-211111140000-2-2-2-200000011-2-20000001100000000000000000000000000
χ4644444-2-2-2-244-2-2-2-24-2-214-2-21-2-211-2-244-4-41111-2-2-2-2-2-2111111-400002222000000-1-122000000-1-100000000000000000000000000
χ4744444-2-2-2-244-2-2-2-24-2-21-4-2-21-2-211-2-2-4-4441111222222-1-1-1-1-1-1-40000-2-2-2-20000001122000000-1-100000000000000000000000000
χ4844444-2-2-2-244-2-2-2-24-2-21-4-2-21-2-211-2-2-4-4-4-41111222222-1-1-1-1-1-1400002222000000-1-1-2-20000001100000000000000000000000000
χ494444-24-24-2-2-24-24-2-2-21-24-21-2-21-2-2-21-2-20011114-2-2-211-2-2111100044000000-2-20000000-200-2-20000001111000000000000000000
χ504444-24-24-2-2-24-24-2-2-21-24-21-2-21-2-2-21-2-20011114-2-2-211-2-21111000-4-400000022000000020022000000-1-1-1-1000000000000000000
χ514444-24-24-2-2-24-24-2-2-21-2-4-21-2-21-2-2-2122001111-4222-1-122-1-1-1-10004-4000000-2-20000000200-2200000011-1-1000000000000000000
χ524444-24-24-2-2-24-24-2-2-21-2-4-21-2-21-2-2-2122001111-4222-1-122-1-1-1-1000-44000000220000000-2002-2000000-1-111000000000000000000
χ534444-2-24-24-2-2-24-24-21-2-241-2-21-2-2-21-2-2-2001111-2411-2-2-2-21111044000000-2-200000000-20-2-2000011110000000000000000000000
χ544444-2-24-24-2-2-24-24-21-2-241-2-21-2-2-21-2-2-2001111-2411-2-2-2-211110-4-4000000220000000020220000-1-1-1-10000000000000000000000
χ554444-2-24-24-2-2-24-24-21-2-2-41-2-21-2-2-21-2220011112-4-1-12222-1-1-1-104-4000000-2-20000000020-22000011-1-10000000000000000000000
χ564444-2-24-24-2-2-24-24-21-2-2-41-2-21-2-2-21-2220011112-4-1-12222-1-1-1-10-440000002200000000-202-20000-1-1110000000000000000000000
χ5744-4-444-24-2-44-42-42-44-2-204-2-2-4222-42004-4-2-222000000000000000004-4-22000000-22000000000000000000000000000000000000
χ5844-4-444-24-2-44-42-42-44-2-204-2-2-4222-4200-44-2-22200000000000000000-442-20000002-2000000000000000000000000000000000000
χ5944-4-44-24-24-442-42-4-4-24-20-24-22-4222-4004-4-2-22200000000000000000-224-4000000-22000000000000000000000000000000000000
χ6044-4-44-24-24-442-42-4-4-24-20-24-22-4222-400-44-2-222000000000000000002-2-440000002-2000000000000000000000000000000000000
χ6144-4-44-2-2-2-2-442222-4-2-210-2-2122-1-122004-411-1-10000003i−3i3i3i−3i−3i00000-22-220000001-1000000003i−3i00000000000000000000000000
χ6244-4-44-2-2-2-2-442222-4-2-210-2-2122-1-122004-411-1-1000000−3i3i−3i−3i3i3i00000-22-220000001-100000000−3i3i00000000000000000000000000
χ6344-4-44-2-2-2-2-442222-4-2-210-2-2122-1-12200-4411-1-10000003i−3i3i3i−3i−3i000002-22-2000000-1100000000−3i3i00000000000000000000000000
χ6444-4-44-2-2-2-2-442222-4-2-210-2-2122-1-12200-4411-1-1000000−3i3i−3i−3i3i3i000002-22-2000000-11000000003i−3i00000000000000000000000000
χ6544-4-4-244442-2-4-4-4-42-2-240-2-2422-4-4220000-2-22200000000000000000000000004-40000000000000000000000000-2200000000000
χ6644-4-4-244442-2-4-4-4-42-2-240-2-2422-4-4220000-2-2220000000000000000000000000-4400000000000000000000000002-200000000000
χ674-44-4444-4-4-4-4-4-44444440-4-4-4-4-4-444400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-42-4-4-424-244-2-20-422-422-24-20000-22-2200000000000000000000000000000000000000000000000000000000−2i32i30000000
χ694-44-444-2-42-4-4-424-244-2-20-422-422-24-20000-22-22000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ704-44-44-242-4-4-42-4-244-24-202-422-42-2-240000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ714-44-44-242-4-4-42-4-244-24-202-422-42-2-240000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ724-44-4-244-4-422-4-444-2-2-24022-422-44-2-20000-22-220000000000000000000000000000000000000000000000000000000000−2i32i300000
χ734-44-4-244-4-422-4-444-2-2-24022-422-44-2-20000-22-2200000000000000000000000000000000000000000000000000000000002i3−2i300000
χ744-4-44444-4-44-444-4-4-44440-4-4-4444-4-4-400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-424-44-2-42-44-2-20-4224-2-22-420000-222-20000000000000000000000023−2300000000000000000023−2300000000000000000000
χ764-4-4444-2-424-44-2-42-44-2-20-4224-2-22-420000-222-200000000000000000000000−2323000000000000000000−232300000000000000000000
χ774-4-444-242-44-4-242-4-4-24-202-42-24-222-40000-222-200000000000000000000023−23000000000000000023−23000000000000000000000000
χ784-4-444-242-44-4-242-4-4-24-202-42-24-222-40000-222-2000000000000000000000−23230000000000000000−2323000000000000000000000000
χ794-4-44-244-4-4-2244-4-42-2-24022-4-2-24-422−2i32i300-222-200−2i32i3−2i32i300−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ804-4-44-244-4-4-2244-4-42-2-24022-4-2-24-4222i3−2i300-222-2002i3−2i32i3−2i3002i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ814-4-44-24-2-42-224-2-422-21-202-12-21-222-1−2i32i3001-1-1100−2i32i3i3−i300i3−i3i3−i30000000000023−23000000000000000000−333i−3i000000000000000000
χ824-4-44-24-2-42-224-2-422-21-202-12-21-222-1−2i32i3001-1-1100−2i32i3i3−i300i3−i3i3−i300000000000−23230000000000000000003−3−3i3i000000000000000000
χ834-4-44-24-2-42-224-2-422-21-202-12-21-222-12i3−2i3001-1-11002i3−2i3−i3i300−i3i3−i3i30000000000023−23000000000000000000−33−3i3i000000000000000000
χ844-4-44-24-2-42-224-2-422-21-202-12-21-222-12i3−2i3001-1-11002i3−2i3−i3i300−i3i3−i3i300000000000−23230000000000000000003−33i−3i000000000000000000
χ854-4-44-2-242-4-22-242-421-2-20-1221-2-22-12−2i32i3001-1-1100i3−i3−2i32i300i3−i3i3−i300000000023−230000000000000000−333i−3i0000000000000000000000
χ864-4-44-2-242-4-22-242-421-2-20-1221-2-22-12−2i32i3001-1-1100i3−i3−2i32i300i3−i3i3−i3000000000−232300000000000000003−3−3i3i0000000000000000000000
χ874-4-44-2-242-4-22-242-421-2-20-1221-2-22-122i3−2i3001-1-1100−i3i32i3−2i300−i3i3−i3i300000000023−230000000000000000−33−3i3i0000000000000000000000
χ884-4-44-2-242-4-22-242-421-2-20-1221-2-22-122i3−2i3001-1-1100−i3i32i3−2i300−i3i3−i3i3000000000−232300000000000000003−33i−3i0000000000000000000000
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
χ9188-8-8-48-48-44-4-84-844-42-40-42-44-2444-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-484-44-84-842-4-402-4-4-2444-24000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-44-4444442220222-2-2-2-2-2-20000-1-1110000006i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-44-4444442220222-2-2-2-2-2-20000-1-111000000−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000
χ958-88-88-4-444-8-844-4-48-4-42044-244-22-4-400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-8444-848-4-4-42-404-244-24-4-4200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-484-8444-8-48-42-4-40-244-244-42-400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-22220000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-22220000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000
χ1008-8-888-4-4448-8-4-444-8-4-42044-2-4-42-24400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-44-4-44442220-2-2-2222-2-2-2−4i34i300-111-1002i3−2i32i3−2i300−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-44-4-44442220-2-2-2222-2-2-24i3−4i300-111-100−2i32i3−2i32i300i3−i3i3−i300000000000000000000000000000000000000000000000000000

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