Finite Group Databasebeta

← Group #13168632

Character table — Group #13168632

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122444446612121212121244444466612121212121212121212121212121212122246612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-111111-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111-11-1-1
χ31111111111111111111111111111111111111111111111111-1-111111111-1-1-1-111-1-1111-1-11111-111-1-1-1-111111-1-1-1-111-1-1-1-11-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111
χ511111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-111111-11-1-111111111-11-111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-1-1-11-1-11111-1-1-1-11-1-1-1-111-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111-1111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-111-1-1111111-1-1-1-11111-1-11-1-1-1-1-111-1-111-1-111-111-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1111111111111-11-11-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-11-1
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-111-1-1-1-1-1-111111-11-11-1-11-1-1-1-11111-1-11-11-1-1-1-111-1-1111-1
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-1-1-1-1-1-1-111-1-1111-111-11-11-1-1-1-111-1-111-1111111-1-1-1-1-11-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1111111-1-111-1-1-1-1-11-1-11-11-11111-1-111-1-1-1111111-1-1-1-1-111-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-111-1-1-1-111-1-1-11-11-111-11111-1-1-1-1111-11-1-1-1-111-1-111-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11111-1-1111111-1-1-1-11-11-11111-1-11111-1-1-1-1-1-1-1111111-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-111-111111-1-111-1-11111-111-1-1-1-1111-11-1
χ17222222-122-12-1-12222-1-122-1-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-122002222-1-1-1-100002200-1-1-100-12220-1-10000-1-1-1-120000-1-10000-1000
χ18222222-122-12-1-12222-1-122-1-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-12200-2-222-1-1110000-2-200-1-1-1001-2-220-1-100001111-200001100001000
χ19222222-122-12-1-12222-1-122-1-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-20022-2-211-1-10000-2-20011100-122-20110000-1-1-1-1-200001100001000
χ20222222-122-12-1-12222-1-122-1-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-200-2-2-2-2111100002200111001-2-2-20110000111120000-1-10000-1000
χ21222222-122-12-1-12222-1-1-22-1-1-12-1-12-1-2-2-1-1-1-11-2-2-2111111112-2002-22211-1-10000-2-200-1-1-10012-2-20110000-1-11120000110000-1000
χ22222222-122-12-1-12222-1-1-22-1-1-12-1-12-1-2-2-1-1-1-11-2-2-2111111112-200-2222111100002200-1-1-100-1-22-2011000011-1-1-20000-1-100001000
χ23222222-122-12-1-12222-1-1-22-1-1-12-1-12-1-2-2-1-1-1-11-2-2-211111111-22002-2-2-2-1-1-1-1000022001110012-220-1-10000-1-111-20000-1-100001000
χ24222222-122-12-1-12222-1-1-22-1-1-12-1-12-1-2-2-1-1-1-11-2-2-211111111-2200-22-2-2-1-1110000-2-20011100-1-2220-1-1000011-1-120000110000-1000
χ2522222-122-12-1222-12-1-122-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100222200002222000022000-1-12-1-10200-1-1-1-1-1-1-1-1020-1-100-1-1000000
χ2622222-122-12-1222-12-1-122-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10022-2-20000-2-2220000-2-2000-1-1-2110200-1-1-1-111110-20110011000000
χ2722222-122-12-1222-12-1-122-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100-2-222000022-2-20000-2-2000112-1-10-2001111-1-1-1-10-20110011000000
χ2822222-122-12-1222-12-1-122-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100-2-2-2-20000-2-2-2-200002200011-2110-20011111111020-1-100-1-1000000
χ2922222-122-12-1222-12-1-12-2-1-1-12-122-1-111-1-1-1-1-2-211-2-2111111002-22-2000022220000-2-2000-11-2-110-200-1-111-1-111020-1-10011000000
χ3022222-122-12-1222-12-1-12-2-1-1-12-122-1-111-1-1-1-1-2-211-2-2111111002-2-220000-2-222000022000-1121-10-200-1-11111-1-10-201100-1-1000000
χ3122222-122-12-1222-12-1-12-2-1-1-12-122-1-111-1-1-1-1-2-211-2-211111100-222-2000022-2-20000220001-1-2-11020011-1-1-1-1110-201100-1-1000000
χ3222222-122-12-1222-12-1-12-2-1-1-12-122-1-111-1-1-1-1-2-211-2-211111100-22-220000-2-2-2-20000-2-20001-121-1020011-1-111-1-1020-1-10011000000
χ332222-122-122222-12-1-12-12-122-1-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1222200-1-12200-1-12200002-1-122000-1-1-1-1-1-1-1-10000002000000-1-10-100
χ342222-122-122222-12-1-12-12-122-1-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-122-2-200-1-1220011-2-200002-1-1-2-2000-11-1-11111000000-2000000110100
χ352222-122-122222-12-1-12-12-122-1-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2220011-2-200-1-1-2-20000-211220001-111-1-1-1-1000000-2000000110100
χ362222-122-122222-12-1-12-12-122-1-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2-20011-2-20011220000-211-2-2000111111110000002000000-1-10-100
χ372222-122-122222-12-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-1-211111-2-211112-22-200-1-1-2-200-1-12200002-1-12-20001111-1-111000000-2000000-1-10100
χ382222-122-122222-12-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-1-211111-2-211112-2-2200-1-1-2-20011-2-200002-1-1-220001-11111-1-10000002000000110-100
χ392222-122-122222-12-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-1-211111-2-21111-222-200112200-1-1-2-20000-2112-2000-11-1-1-1-1110000002000000110-100
χ402222-122-122222-12-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-1-211111-2-21111-22-220011220011220000-211-22000-1-1-1-111-1-1000000-2000000-1-10100
χ4122-2-2222-2-222-2-2-2-222220-22-2-2-2-222-20022-2-2000000000000000000000000002-22i−2i2i−2i00000000000000000000000002i−2i2i−2i2-20000
χ4222-2-2222-2-222-2-2-2-222220-22-2-2-2-222-20022-2-2000000000000000000000000002-2−2i2i−2i2i0000000000000000000000000−2i2i−2i2i2-20000
χ4322-2-2222-2-222-2-2-2-222220-22-2-2-2-222-20022-2-200000000000000000000000000-222i−2i−2i2i00000000000000000000000002i−2i−2i2i-220000
χ4422-2-2222-2-222-2-2-2-222220-22-2-2-2-222-20022-2-200000000000000000000000000-22−2i2i2i−2i0000000000000000000000000−2i2i2i−2i-220000
χ4544444-2-24-2-2-2-2-24-24-21-24-211-2-2-2-2-21-2-21111-24-2-2-2-21111110000440000-2-20000000000000-2-2-2000000001111000000000000000
χ4644444-2-24-2-2-2-2-24-24-21-24-211-2-2-2-2-21-2-21111-24-2-2-2-21111110000-4-4000022000000000000022200000000-1-1-1-1000000000000000
χ4744444-2-24-2-2-2-2-24-24-21-2-4-211-2-2-2-2-212211112-42222-1-1-1-1-1-100004-40000-2-200000000000002-220000000011-1-1000000000000000
χ4844444-2-24-2-2-2-2-24-24-21-2-4-211-2-2-2-2-212211112-42222-1-1-1-1-1-10000-440000220000000000000-22-200000000-1-111000000000000000
χ494444-24-2-24-24-2-2-24-2-2-214-2-2-21-211-2-2441111-2-2-2-211-2-21111440000-2-2-2-20000000000-21100000-201100000000000000000000000
χ504444-24-2-24-24-2-2-24-2-2-214-2-2-21-211-2-2441111-2-2-2-211-2-21111-4-40000222200000000002-1-10000020-1-100000000000000000000000
χ514444-24-2-24-24-2-2-24-2-2-21-4-2-2-21-211-2-2-4-411112222-1-122-1-1-1-14-40000-2-2220000000000-2110000020-1-100000000000000000000000
χ524444-24-2-24-24-2-2-24-2-2-21-4-2-2-21-211-2-2-4-411112222-1-122-1-1-1-1-44000022-2-200000000002-1-100000-201100000000000000000000000
χ534444-2-24-2-24-244-2-2-21-2-241-2-2-21-2-21-2-2-211114-211-2-2-2-21111004400000000-2-2000000000-2-20000-20011110000000000000000000
χ544444-2-24-2-24-244-2-2-21-2-241-2-2-21-2-21-2-2-211114-211-2-2-2-2111100-4-40000000022000000000220000200-1-1-1-10000000000000000000
χ554444-2-24-2-24-244-2-2-21-2-2-41-2-2-21-2-21-2221111-42-1-12222-1-1-1-1004-400000000-2-2000000000-22000020011-1-10000000000000000000
χ564444-2-24-2-24-244-2-2-21-2-2-41-2-2-21-2-21-2221111-42-1-12222-1-1-1-100-4400000000220000000002-20000-200-1-1110000000000000000000
χ5744-4-444-2-4-4-2422-4-444-2-20-4-222-42-24200-2-22200000000000000000000000000004i−4i000000000000000000000000000−2i2i00000000
χ5844-4-444-2-4-4-2422-4-444-2-20-4-222-42-24200-2-2220000000000000000000000000000−4i4i0000000000000000000000000002i−2i00000000
χ5944-4-44-24-424-2-4-4-424-2-2402-22-42-44-2200-2-2220000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ6044-4-44-24-424-2-4-4-424-2-2402-22-42-44-2200-2-222000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ6144-4-4-2442-444-4-42-4-2-24-2024-4222-2-2-400-2-222000000000000000000000000004-4000000000000000000000000000000000-220000
χ6244-4-4-2442-444-4-42-4-2-24-2024-4222-2-2-400-2-22200000000000000000000000000-440000000000000000000000000000000002-20000
χ634-44-444444-4-4-44-4-4-444404-444-4-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-2442-42-2-4-4-44-2-2042-2-2-422-4200-22-220000000000000000000023−230000000000000000000023−2300000000000000000000000
χ654-44-444-2442-42-2-4-4-44-2-2042-2-2-422-4200-22-2200000000000000000000−232300000000000000000000−232300000000000000000000000
χ664-44-44-244-2-42-44-42-4-2-240-22-242-4-42200-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ674-44-44-244-2-42-44-42-4-2-240-22-242-4-42200-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ684-44-4-244-24-4-4-442-42-24-20-2-44-22222-400-22-22000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ694-44-4-244-24-4-4-442-42-24-20-2-44-22222-400-22-220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ704-44-4-24-2-242-42-22-42-2-210-22-212-1-122001-11-100003i−3i003i3i−3i−3i000000−2i32i323−2300000000000i3−i30000000−3300000000000000000000000
χ714-44-4-24-2-242-42-22-42-2-210-22-212-1-122001-11-100003i−3i003i3i−3i−3i0000002i3−2i3−232300000000000−i3i300000003−300000000000000000000000
χ724-44-4-24-2-242-42-22-42-2-210-22-212-1-122001-11-10000−3i3i00−3i−3i3i3i000000−2i32i3−232300000000000i3−i300000003−300000000000000000000000
χ734-44-4-24-2-242-42-22-42-2-210-22-212-1-122001-11-10000−3i3i00−3i−3i3i3i0000002i3−2i323−2300000000000−i3i30000000−3300000000000000000000000
χ744-4-44444-4-4-4-44-444-44440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-4-42-4-2244-44-2-20-42224-22-4-200-222-20000000000000000000000−2i32i3000000000000000000000000−2i32i300000000000000000
χ764-4-4444-2-4-42-4-2244-44-2-20-42224-22-4-200-222-200000000000000000000002i3−2i30000000000000000000000002i3−2i300000000000000000
χ774-4-444-24-42-424-44-2-4-2-240222-4-24-42-2−2i32i3-222-200−2i32i300−2i32i3−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ784-4-444-24-42-424-44-2-4-2-240222-4-24-42-22i3−2i3-222-2002i3−2i3002i3−2i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ794-4-444-2-2-4222-224-2-4-21-202-1-12-2-2221−2i32i31-1-1100−2i32i300i3−i3i3−i3i3−i30000000000−2i32i3000000000000000000000000i3−i33-3000000000000000
χ804-4-444-2-2-4222-224-2-4-21-202-1-12-2-2221−2i32i31-1-1100−2i32i300i3−i3i3−i3i3−i300000000002i3−2i3000000000000000000000000−i3i3-33000000000000000
χ814-4-444-2-2-4222-224-2-4-21-202-1-12-2-22212i3−2i31-1-11002i3−2i300−i3i3−i3i3−i3i30000000000−2i32i3000000000000000000000000i3−i3-33000000000000000
χ824-4-444-2-2-4222-224-2-4-21-202-1-12-2-22212i3−2i31-1-11002i3−2i300−i3i3−i3i3−i3i300000000002i3−2i3000000000000000000000000−i3i33-3000000000000000
χ834-4-44-2442-4-4-44-4-242-24-202-4-42-2-222400-222-200000000000000000000000023−2300000000000000000023−23000000000000000000000
χ844-4-44-2442-4-4-44-4-242-24-202-4-42-2-222400-222-2000000000000000000000000−2323000000000000000000−2323000000000000000000000
χ854-4-44-2-2422-424-4-2-221-2-20-12221-22-1-2−2i32i31-1-1100i3−i300−2i32i3i3−i3i3−i300000000000023−23000000000000000000−333i−3i0000000000000000000
χ864-4-44-2-2422-424-4-2-221-2-20-12221-22-1-2−2i32i31-1-1100i3−i300−2i32i3i3−i3i3−i3000000000000−23230000000000000000003−3−3i3i0000000000000000000
χ874-4-44-2-2422-424-4-2-221-2-20-12221-22-1-22i3−2i31-1-1100−i3i3002i3−2i3−i3i3−i3i300000000000023−23000000000000000000−33−3i3i0000000000000000000
χ884-4-44-2-2422-424-4-2-221-2-20-12221-22-1-22i3−2i31-1-1100−i3i3002i3−2i3−i3i3−i3i3000000000000−23230000000000000000003−33i−3i0000000000000000000
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
χ9188-8-88-4-4-84-4-444-848-42-4042-2444-4-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-8-48444-8-4-4-4204-44-24-22-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48448-4-8-844-42-4-40-2-444-24-4240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-4-44444-42220-22-2-2-2-222-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-444-4-44444-42220-22-2-2-2-222-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ968-88-88-4-48-4444-4-84-8-42-40-4-22-44444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-4-4-84-884442-4-4024-4-4-244-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4-4444-444422202-222-2-2-2-2-200-11-1100006i−6i00−3i−3i3i3i0000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-4-4444-444422202-222-2-2-2-2-200-11-110000−6i6i003i3i−3i−3i0000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-84-8-44-484-4-420444-2-42-24-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44444-44-4-442220-2-2-2-222-2-22−4i34i3-111-1002i3−2i3002i3−2i3−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44444-44-4-442220-2-2-2-222-2-224i3−4i3-111-100−2i32i300−2i32i3i3−i3i3−i30000000000000000000000000000000000000000000000000000000

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