Finite Group Databasebeta

← Group #13168115

Character table — Group #13168115

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612123666121212121212121212121212222444666666121222444466666666612121212121212121212122446612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-11111-1-111-1-111-1-111-11111-1-111-11-11111-1-1-11-1-1-1-1-1-1-111-11-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111111111-1-1-1-11-1111-1-1111-11-1111-1-1111-1-111-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-111-1-1-1-1111-1-111-1-1-1-11-1-1-1-111-1-1-1-1-1-11-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111-111-11111-1-111-1-1-1-1-1-111-111-1-11111-11111-1-11111-1-11-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-111-1-1-1-1-1-111-1-1-1-1-11-1-1-111-1-1-11-11-1-1-111-1-11-1-111-1-1-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-111-1-11-11-1-1-1-111-11-1-1-1-1-1-1-111-1111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-11111-11111-1-1-1-11-11-1-1-1-11111-1-1-111-1-1-1-111-11
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-11111-1-11111111-1111-1-111-11-11-1-1-111-1-1-1-1-11111-1-111-1-1-11
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-111-1-11-1-111-1-1-1-1-11111-1-111111-11-1-1-1-111111-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-111-1-1-111-1-111111-1-1-1-111-1-1-1-11-11-1-1-1-111111-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-111111111-11-1-1-111-1-11-11-1111-1-111-1-1-11111-1-111-1-11-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-11111-11-11111-1-111-1-1-111-1-1-1-1111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11111-1-111-1-1-11-11
χ17222222-122-12-1-12222-1-122-1-12-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-120220200-1-1-1-122220000202-1-100-1-1-10-102-1-100-1-1200-1-1000000-1000
χ18222222-122-12-1-12222-1-122-1-12-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-120-220-200-1-11122-2-2000020-2-1-10011-1010-2-1-10011-200110000001000
χ19222222-122-12-1-12222-1-122-1-12-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-202-2020011-1-1-2-2-2-20000-2021100-1-110-1021100-1-1-200110000001000
χ20222222-122-12-1-12222-1-122-1-12-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-20-2001111-2-2220000-20-21100111010-2110011200-1-1000000-1000
χ21222222-122-12-1-12222-1-1-22-1-12-1-12-1-1-2-2-1-1-1-1-21-2-211111111202-20-200-1-1-1-1-2-2220000202-1-100-1-11010-2110011-200-1-10000001000
χ22222222-122-12-1-12222-1-1-22-1-12-1-12-1-1-2-2-1-1-1-1-21-2-21111111120-2-20200-1-111-2-2-2-2000020-2-1-1001110-1021100-1-120011000000-1000
χ23222222-122-12-1-12222-1-1-22-1-12-1-12-1-1-2-2-1-1-1-1-21-2-211111111-20220-20011-1-122-2-20000-2021100-1-1-1010-2-1-1001120011000000-1000
χ24222222-122-12-1-12222-1-1-22-1-12-1-12-1-1-2-2-1-1-1-1-21-2-211111111-20-220200111122220000-20-2110011-10-102-1-100-1-1-200-1-10000001000
χ2522222-122-12222-1-12-12-12-12-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1022022220022000000220-1-100-1-1-1-1022-1-100-1-1-1-100200-1-1-1-1000000
χ2622222-122-12222-1-12-12-12-12-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-102-202-22200-2-2000000-2-20-1100-1-11102-2-1100-1-11100-2001111000000
χ2722222-122-12222-1-12-12-12-12-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10-220-22-2-20022000000-2-201-10011-1-10-221-10011-1-100-2001111000000
χ2822222-122-12222-1-12-12-12-12-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10-2-20-2-2-2-200-2-2000000220110011110-2-21100111100200-1-1-1-1000000
χ2922222-122-12222-1-12-12-1-2-12-1-12-1-12-111-1-1-1-1-2-211-2-21111110220-2-2220022000000-2-20-1-100-1-1-1-10-2-2110011110020011-1-1000000
χ3022222-122-12222-1-12-12-1-2-12-1-12-1-12-111-1-1-1-1-2-211-2-211111102-20-222200-2-2000000220-1100-1-1110-221-10011-1-100-200-1-111000000
χ3122222-122-12222-1-12-12-1-2-12-1-12-1-12-111-1-1-1-1-2-211-2-21111110-2202-2-2-200220000002201-10011-1-102-2-1100-1-11100-200-1-111000000
χ3222222-122-12222-1-12-12-1-2-12-1-12-1-12-111-1-1-1-1-2-211-2-21111110-2-2022-2-200-2-2000000-2-2011001111022-1-100-1-1-1-10020011-1-1000000
χ332222-122-122-12222-1-1-122-1-12-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1220220-1-12200-1-1002200-120-1-1-1-1002-1020-1-1-1-100020000000-1-10-100
χ342222-122-122-12222-1-1-122-1-12-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-12-202-20112200-1-100-2-200-1-20-1-11100210-20-1-111000-20000000110100
χ352222-122-122-12222-1-1-122-1-12-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-220-220-1-1-2-2001100-2-20012011-1-100-2-102011-1-1000-20000000110100
χ362222-122-122-12222-1-1-122-1-12-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-2011-2-200110022001-20111100-210-20111100020000000-1-10-100
χ372222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-2-1-1-1-11-21111-2-21111220-2-20-1-122001100-2-200-120-1-1-1-100-210-20111100020000000110-100
χ382222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-2-1-1-1-11-21111-2-211112-20-22011220011002200-1-20-1-11100-2-102011-1-1000-20000000-1-10100
χ392222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-2-1-1-1-11-21111-2-21111-2202-20-1-1-2-200-1-100220012011-1-100210-20-1-111000-20000000-1-10100
χ402222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-2-1-1-1-11-21111-2-21111-2-2022011-2-200-1-100-2-2001-201111002-1020-1-1-1-100020000000110-100
χ4122-2-2222222-2-2-2-2-2-22220-2-2-2222-2-2-2002-2-22000000000000000000000000002-22i−2i2i−2i000000000000000000000002-22i−2i002i−2i0000
χ4222-2-2222222-2-2-2-2-2-22220-2-2-2222-2-2-2002-2-22000000000000000000000000002-2−2i2i−2i2i000000000000000000000002-2−2i2i00−2i2i0000
χ4322-2-2222222-2-2-2-2-2-22220-2-2-2222-2-2-2002-2-2200000000000000000000000000-222i−2i−2i2i00000000000000000000000-22−2i2i002i−2i0000
χ4422-2-2222222-2-2-2-2-2-22220-2-2-2222-2-2-2002-2-2200000000000000000000000000-22−2i2i2i−2i00000000000000000000000-222i−2i00−2i2i0000
χ4544444-2-24-2-24-2-2-2-24-2-214-2-21-2-21-2-21-2-211114-2-2-2-2-21111110040040000-2-20000000000-200001100-20-2000011000000000000000
χ4644444-2-24-2-24-2-2-2-24-2-214-2-21-2-21-2-21-2-211114-2-2-2-2-211111100-400-4000022000000000020000-1-1002020000-1-1000000000000000
χ4744444-2-24-2-24-2-2-2-24-2-21-4-2-21-2-21-2-21221111-422222-1-1-1-1-1-100400-40000-2-20000000000-2000011002020000-1-1000000000000000
χ4844444-2-24-2-24-2-2-2-24-2-21-4-2-21-2-21-2-21221111-422222-1-1-1-1-1-100-4004000022000000000020000-1-100-20-2000011000000000000000
χ494444-24-2-24-2-2-2-244-2-21-24-21-2-21-2-21-2441111-2-2-2-211-2-2111140040000-2-200-2-2000000-200110000-20000110000000000000000000
χ504444-24-2-24-2-2-2-244-2-21-24-21-2-21-2-21-2441111-2-2-2-211-2-21111-400-40000220022000000200-1-1000020000-1-10000000000000000000
χ514444-24-2-24-2-2-2-244-2-21-2-4-21-2-21-2-21-2-4-411112222-1-122-1-1-1-1400-40000-2-20022000000-20011000020000-1-10000000000000000000
χ524444-24-2-24-2-2-2-244-2-21-2-4-21-2-21-2-21-2-4-411112222-1-122-1-1-1-1-400400002200-2-2000000200-1-10000-20000110000000000000000000
χ534444-2-24-2-24-244-2-2-21-2-241-2-21-2-21-2-2-2-21111-2411-2-2-2-21111040040-2-20000000000000-200011000-20-20001100000000000000000
χ544444-2-24-2-24-244-2-2-21-2-241-2-21-2-21-2-2-2-21111-2411-2-2-2-211110-400-402200000000000002000-1-1000202000-1-100000000000000000
χ554444-2-24-2-24-244-2-2-21-2-2-41-2-21-2-21-2-22211112-4-1-12222-1-1-1-10400-40-2-20000000000000-200011000202000-1-100000000000000000
χ564444-2-24-2-24-244-2-2-21-2-2-41-2-21-2-21-2-22211112-4-1-12222-1-1-1-10-400402200000000000002000-1-1000-20-20001100000000000000000
χ5744-4-444-244-2-422-4-4-44-2-20-4224-2-2-42200-222-2000000000000000000000000004-4000000000000000000000000000-220000000000
χ5844-4-444-244-2-422-4-4-44-2-20-4224-2-2-42200-222-200000000000000000000000000-440000000000000000000000000002-20000000000
χ5944-4-44-244-24-4-4-422-4-24-202-42-24-22-4200-222-20000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ6044-4-44-244-24-4-4-422-4-24-202-42-24-22-4200-222-2000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ6144-4-4-244-2442-4-4-4-42-2-24022-4-2-2422-400-222-200000000000000000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ6244-4-4-244-2442-4-4-4-42-2-24022-4-2-2422-400-222-20000000000000000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ634-44-4444-4-4-4-44-44-4444404-44-4-4-4-44-40044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-2-4-42-4-224-444-2-2042-2-422-4-2200-2-2220000000000000000000000−2i32i3000000000000000−2i32i300000000000000000000000000
χ654-44-444-2-4-42-4-224-444-2-2042-2-422-4-2200-2-22200000000000000000000002i3−2i30000000000000002i3−2i300000000000000000000000000
χ664-44-44-24-42-4-44-4-224-24-20-2-4-22-4224223−23-2-2220023−230023−232323−23−230000000000000000000000000000000000000000000000000000000
χ674-44-44-24-42-4-44-4-224-24-20-2-4-22-42242−2323-2-22200−232300−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ684-44-44-2-2-422-4-22-224-2-210-22122-12-2-123−2311-1-10023−2300−33−3−3330000000000−2i32i3000000000000000i3−i30000000003i−3i000000000000000
χ694-44-44-2-2-422-4-22-224-2-210-22122-12-2-123−2311-1-10023−2300−33−3−33300000000002i3−2i3000000000000000−i3i3000000000−3i3i000000000000000
χ704-44-44-2-2-422-4-22-224-2-210-22122-12-2-1−232311-1-100−2323003−333−3−30000000000−2i32i3000000000000000i3−i3000000000−3i3i000000000000000
χ714-44-44-2-2-422-4-22-224-2-210-22122-12-2-1−232311-1-100−2323003−333−3−300000000002i3−2i3000000000000000−i3i30000000003i−3i000000000000000
χ724-44-4-2442-4-424-44-4-2-2-240-22422-42-2-400-2-222000000000000000000−2i32i300000000000000000−2i32i30000000000000000000000000000
χ734-44-4-2442-4-424-44-4-2-2-240-22422-42-2-400-2-2220000000000000000002i3−2i3000000000000000002i3−2i30000000000000000000000000000
χ744-44-4-2-2422-424-4-22-21-2-2012-2-122-1-2223−2311-1-100−330023−23−3−333000000−2i32i300000000000000000i3−i30000000003i−3i00000000000000000
χ754-44-4-2-2422-424-4-22-21-2-2012-2-122-1-2223−2311-1-100−330023−23−3−3330000002i3−2i300000000000000000−i3i3000000000−3i3i00000000000000000
χ764-44-4-2-2422-424-4-22-21-2-2012-2-122-1-22−232311-1-1003−300−232333−3−3000000−2i32i300000000000000000i3−i3000000000−3i3i00000000000000000
χ774-44-4-2-2422-424-4-22-21-2-2012-2-122-1-22−232311-1-1003−300−232333−3−30000002i3−2i300000000000000000−i3i30000000003i−3i00000000000000000
χ784-4-44444-4-4-44-44-44-44440-44-4-4-4-44-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-4242-2-44-44-2-20-4-22-42242-200-22-2200000000000000000000−2i32i30000000000000−2i32i3000000000000000000000000000000
χ804-4-4444-2-4-4242-2-44-44-2-20-4-22-42242-200-22-22000000000000000000002i3−2i300000000000002i3−2i3000000000000000000000000000000
χ814-4-444-24-42-44-442-2-4-24-202422-42-2-4-200-22-2200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ824-4-444-24-42-44-442-2-4-24-202422-42-2-4-200-22-22000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ834-4-44-2442-4-4-2-44-442-2-2402-2-422-4-22400-22-2200000000000000000000000023−230000000000000000000023−230000000000000000000
χ844-4-44-2442-4-4-2-44-442-2-2402-2-422-4-22400-22-22000000000000000000000000−232300000000000000000000−23230000000000000000000
χ854-4-44-24-22-42-22-2-442-21-202122-12-2-1-2001-11-100003i−3i003i−3i3i−3i00000000−2i32i30023−23000000000i3−i3000000000−330000000000000000000
χ864-4-44-24-22-42-22-2-442-21-202122-12-2-1-2001-11-100003i−3i003i−3i3i−3i000000002i3−2i300−2323000000000−i3i30000000003−30000000000000000000
χ874-4-44-24-22-42-22-2-442-21-202122-12-2-1-2001-11-10000−3i3i00−3i3i−3i3i00000000−2i32i300−2323000000000i3−i30000000003−30000000000000000000
χ884-4-44-24-22-42-22-2-442-21-202122-12-2-1-2001-11-10000−3i3i00−3i3i−3i3i000000002i3−2i30023−23000000000−i3i3000000000−330000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-48-4-4-84444-8-4-42044-2-4-4244-2002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-48-4444-8-84-42-404-24-42-44-24002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-4-484-8-84442-4-40-2442-4-4-244002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-4-44444442220-2-2-2222-2-2-200-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-4-4-44444442220-2-2-2222-2-2-200-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ968-88-8-48-44-844-448-8-4-42-40-4-2-44-244240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-44-44-422202-22-2-2-2-22-243−43-1-11100−232300−232333−3−30000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-44-44-422202-22-2-2-2-22-2−4343-1-1110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-84484-44-4-8-4-4204-4-244-2-442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8-4-884-442-4-40-2-44-24424-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-44-442220-22-2-2-2-22-2200-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-44-442220-22-2-2-2-22-2200-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000

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