Finite Group Databasebeta

← Group #13168631

Character table — Group #13168631

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122224446666121212124444446666666666121212121212121212122246612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-111111111111-1-1-111-1-1-1-1-1-11-1-111-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-1111-1-11-1-11111-1111-1-111111-1-1-1-1-1-111-1-11-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111
χ511111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-111-1-1-111-111-1-1-1-11111111111-11-111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-111-111-1-1-1-11-1-1-111-1-1-1-11-1-1-1-1-1-111-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-11-1-111-1-1-1-1-1111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-111-1-1-1-1-1-1-1-1-1-111-11111111-1-1-1-111-1-1-1-111-11111-1-111-1-1-111-1
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-111-1-111-1-1-11111111-1-1-11-1-1-1-111-1-11-11-1-1-1-1-1-11111-11
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-111-1-1111111-1-1-11-1-111-1-11-11111-1-111-1-1-1-1-1111111-1-1-11
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-1111111-1-1-1-1-1-1-11-1-111-1-111-1-11111-1-111-11111-1-1-1-11-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-1-1-111-1-1-1-1111-111-1-111-1-111-1-1-1-11111-11111-1-1-1-11-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-111111111111-111-1-111-11-1-1-1-111-1-1-1-1-1-1-1111111-1-11-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11111-1-1-1-111-1-11-1-1-1-1-1-1-1111-11111-1-1111-11-1-1-1-1-1-111111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-11111-1-11111-1-1-11111-1-111-1-1-11-11
χ17222222-12-122-122-12-12-12-12-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-122002222-1-100-1-1000022200-100-1-1-1-102-1200-1-1-1-12000000-1-100-1000
χ18222222-12-122-122-12-12-12-12-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-12200-2-222-1-100110000-2-2200-100-1-1-1-10-21-2001111-200000011001000
χ19222222-12-122-122-12-12-12-12-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-20022-2-21100-1-10000-2-2-200100111102-1200-1-1-1-1-200000011001000
χ20222222-12-122-122-12-12-12-12-1-12-1-12-122-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-200-2-2-2-2110011000022-20010011110-21-20011112000000-1-100-1000
χ21222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-11-2-2-2111111112-2002-222110011000022-200-100-1-1110-2-120011-1-1-2000000-1-1001000
χ22222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-11-2-2-2111111112-200-22221100-1-10000-2-2-200-100-1-111021-200-1-11120000001100-1000
χ23222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-11-2-2-211111111-22002-2-2-2-1-100110000-2-220010011-1-10-2-120011-1-120000001100-1000
χ24222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-11-2-2-211111111-2200-22-2-2-1-100-1-100002220010011-1-1021-200-1-111-2000000-1-1001000
χ2522222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10022220000222200220002-10-1-10000-1-12-1-1-1-1-1-1-1020-1-10000-1-10000
χ2622222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10022-2-2000022-2-200-2-20002-10-1-10000-11-21-1-111110-20110000110000
χ2722222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100-2-2220000-2-22200-2-2000-2101100001-12-111-1-1-1-10-20110000110000
χ2822222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100-2-2-2-20000-2-2-2-20022000-21011000011-21111111020-1-10000-1-10000
χ2922222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-2111111002-22-20000-2-2-2-200-2-20002-10-1-10000112-11111-1-1020-1-10000110000
χ3022222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-2111111002-2-220000-2-22200220002-10-1-100001-1-2111-1-1110-20110000-1-10000
χ3122222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-211111100-222-2000022-2-20022000-210110000-112-1-1-111-1-10-20110000-1-10000
χ3222222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-211111100-22-220000222200-2-2000-210110000-1-1-21-1-1-1-111020-1-10000110000
χ332222-122-12222-1-1222-1-122-1-1-1-1-12-1222-1-1-1-12-1-1-1-1-122-1-1-1-1222200-1-122-1-100220000-1-122-1-1-1-1-1-12000-1-1000000200-1-100000-100
χ342222-122-12222-1-1222-1-122-1-1-1-1-12-1222-1-1-1-12-1-1-1-1-122-1-1-1-122-2-200-1-1221100-2-20000-11-2211-1-1-1-1-200011000000-2001100000100
χ352222-122-12222-1-1222-1-122-1-1-1-1-12-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2220011-2-2-1-100-2-200001-12-2-1-111112000-1-1000000-2001100000100
χ362222-122-12222-1-1222-1-122-1-1-1-1-12-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2-20011-2-2110022000011-2-2111111-200011000000200-1-100000-100
χ372222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-1-211111-2-211112-22-200-1-1-2-21100-2-200001-122-1-1-1-111-2000110000002001100000-100
χ382222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-1-211111-2-211112-2-2200-1-1-2-2-1-10022000011-2211-1-1112000-1-1000000-200-1-100000100
χ392222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-1-211111-2-21111-222-20011221100220000-1-12-2-1-111-1-1-200011000000-200-1-100000100
χ402222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-1-211111-2-21111-22-22001122-1-100-2-20000-11-2-21111-1-12000-1-10000002001100000-100
χ4122-2-2222-222-2-2-22-2-222202-22-2-2-2-22-20022-2-2000000000000000000000000002-22i−2i2i−2i00000000000000000000000002-22i−2i2i−2i0000
χ4222-2-2222-222-2-2-22-2-222202-22-2-2-2-22-20022-2-2000000000000000000000000002-2−2i2i−2i2i00000000000000000000000002-2−2i2i−2i2i0000
χ4322-2-2222-222-2-2-22-2-222202-22-2-2-2-22-20022-2-200000000000000000000000000-222i−2i−2i2i0000000000000000000000000-22−2i2i2i−2i0000
χ4422-2-2222-222-2-2-22-2-222202-22-2-2-2-22-20022-2-200000000000000000000000000-22−2i2i2i−2i0000000000000000000000000-222i−2i−2i2i0000
χ4544444-2-24-2-2-2-244-2-21-2-241-2-2-2-2-21-21-2-21111-24-2-2-2-2111111000044000000-2-200000000000000000-2-2-2001111000000000000000
χ4644444-2-24-2-2-2-244-2-21-2-241-2-2-2-2-21-21-2-21111-24-2-2-2-21111110000-4-4000000220000000000000000022200-1-1-1-1000000000000000
χ4744444-2-24-2-2-2-244-2-21-2-2-41-2-2-2-2-21-212211112-42222-1-1-1-1-1-100004-400000022000000000000000002-2-200-1-111000000000000000
χ4844444-2-24-2-2-2-244-2-21-2-2-41-2-2-2-2-21-212211112-42222-1-1-1-1-1-10000-44000000-2-200000000000000000-2220011-1-1000000000000000
χ494444-24-2-2-244-2-2-2-24-2-214-2-211-21-2-2-2441111-2-2-2-211-2-21111440000-2-2-2-20000000000-200-20011110000000000000000000000000
χ504444-24-2-2-244-2-2-2-24-2-214-2-211-21-2-2-2441111-2-2-2-211-2-21111-4-4000022220000000000200200-1-1-1-10000000000000000000000000
χ514444-24-2-2-244-2-2-2-24-2-21-4-2-211-21-2-2-2-4-411112222-1-122-1-1-1-14-40000-2-2220000000000200-20011-1-10000000000000000000000000
χ524444-24-2-2-244-2-2-2-24-2-21-4-2-211-21-2-2-2-4-411112222-1-122-1-1-1-1-44000022-2-20000000000-200200-1-1110000000000000000000000000
χ534444-2-24-24-2-24-2-24-2-21-24-21-2-21-2-21-2-2-211114-211-2-2-2-211110044000000-2-2000000000-2-20110000-2000110000000000000000000
χ544444-2-24-24-2-24-2-24-2-21-24-21-2-21-2-21-2-2-211114-211-2-2-2-2111100-4-400000022000000000220-1-100002000-1-10000000000000000000
χ554444-2-24-24-2-24-2-24-2-21-2-4-21-2-21-2-21-2221111-42-1-12222-1-1-1-1004-400000022000000000-2-201100002000-1-10000000000000000000
χ564444-2-24-24-2-24-2-24-2-21-2-4-21-2-21-2-21-2221111-42-1-12222-1-1-1-100-44000000-2-2000000000220-1-10000-2000110000000000000000000
χ5744-4-444-2-4-24-42-442-4-24-20-2-4-22-4224200-2-2220000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ5844-4-444-2-4-24-42-442-4-24-20-2-4-22-4224200-2-222000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ5944-4-44-24-44-22-4-44-42-2-240-224-42-42-2200-2-22200000000000000000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ6044-4-44-24-44-22-4-44-42-2-240-224-42-42-2200-2-2220000000000000000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ6144-4-4-244244-4-42-2-4-44-2-2042-2222-4-2-400-2-222000000000000000000000000004-400000000000000000000000000000-2200000000
χ6244-4-4-244244-4-42-2-4-44-2-2042-2222-4-2-400-2-22200000000000000000000000000-44000000000000000000000000000002-200000000
χ634-44-4444-4-4-4-444-4-444440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-2-42-4-4-24-424-24-202-4224-22-4-200-222-200000000000000000000−2i32i3000000000000000000−2i32i30000000000000000000000000
χ654-44-444-2-42-4-4-24-424-24-202-4224-22-4-200-222-2000000000000000000002i3−2i30000000000000000002i3−2i30000000000000000000000000
χ664-44-44-24-4-42244-4-4-2-2-24022-4-4-2422-200-222-20000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ674-44-44-24-4-42244-4-4-2-2-24022-4-4-2422-200-222-200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ684-44-4-2442-4-4-44-22-444-2-20-4222-2-2-42400-222-2000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000000000
χ694-44-4-2442-4-4-44-22-444-2-20-4222-2-2-42400-222-20000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000000000
χ704-44-4-24-222-4-4-2-2224-2-21022-1-1-2122-2001-1-1100003-30033-3-3000000−2i32i3−2i32i30000000000000000i3−i3i3−i30000000000000000000000000
χ714-44-4-24-222-4-4-2-2224-2-21022-1-1-2122-2001-1-1100003-30033-3-30000002i3−2i32i3−2i30000000000000000−i3i3−i3i30000000000000000000000000
χ724-44-4-24-222-4-4-2-2224-2-21022-1-1-2122-2001-1-110000-3300-3-333000000−2i32i32i3−2i30000000000000000i3−i3−i3i30000000000000000000000000
χ734-44-4-24-222-4-4-2-2224-2-21022-1-1-2122-2001-1-110000-3300-3-3330000002i3−2i3−2i32i30000000000000000−i3i3i3−i30000000000000000000000000
χ744-4-444444-4-44-4-4-44-44440-44-44-4-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-242-442-4-4-2-4-24-20242-2-42-2-4200-22-22000000000000000000000000−2i32i30000000000000000000000−2i32i300000000000000000
χ764-4-4444-242-442-4-4-2-4-24-20242-2-42-2-4200-22-220000000000000000000000002i3−2i300000000000000000000002i3−2i300000000000000000
χ774-4-444-244-42-2-4-4-442-2-2402-2-442-4-22223−23-22-220023−230023−2323−2323−230000000000000000000000000000000000000000000000000000000
χ784-4-444-244-42-2-4-4-442-2-2402-2-442-4-222−2323-22-2200−232300−2323−2323−23230000000000000000000000000000000000000000000000000000000
χ794-4-444-2-2422-22-4-4-221-2-20-1-22-22212-123−231-11-10023−2300−33−33−33000000000000−2i32i30000000000000000000000i3−i33i−3i000000000000000
χ804-4-444-2-2422-22-4-4-221-2-20-1-22-22212-123−231-11-10023−2300−33−33−330000000000002i3−2i30000000000000000000000−i3i3−3i3i000000000000000
χ814-4-444-2-2422-22-4-4-221-2-20-1-22-22212-1−23231-11-100−2323003−33−33−3000000000000−2i32i30000000000000000000000i3−i3−3i3i000000000000000
χ824-4-444-2-2422-22-4-4-221-2-20-1-22-22212-1−23231-11-100−2323003−33−33−30000000000002i3−2i30000000000000000000000−i3i33i−3i000000000000000
χ834-4-44-244-2-4-44-4224-44-2-20-4-22-22242-400-22-22000000000000000000000023−23000000000000000000000023−230000000000000000000
χ844-4-44-244-2-4-44-4224-44-2-20-4-22-22242-400-22-220000000000000000000000−23230000000000000000000000−23230000000000000000000
χ854-4-44-2-24-2-42-2-42242-21-20212-2-12-2-1223−231-11-100−330023−23−33−33000000000023−230000000000003-300000000−330000000000000000000
χ864-4-44-2-24-2-42-2-42242-21-20212-2-12-2-1223−231-11-100−330023−23−33−330000000000−2323000000000000-33000000003−30000000000000000000
χ874-4-44-2-24-2-42-2-42242-21-20212-2-12-2-12−23231-11-1003−300−23233−33−3000000000023−23000000000000-3300000000−330000000000000000000
χ884-4-44-2-24-2-42-2-42242-21-20212-2-12-2-12−23231-11-1003−300−23233−33−30000000000−23230000000000003-3000000003−30000000000000000000
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
χ9188-8-88-4-4-8-4-444-88442-4-4024-4444-2-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-48-844-44-8-4-420-442-24-24-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4848-44-84-4-84-42-40-4-2-44-244240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-4444-44422202-22-2-2-2-22-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-4-4444-44422202-22-2-2-2-22-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ968-88-88-4-4-8444-48-84-42-4-40-2444-4-4-242002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-484-8448-44-8-4-42-404-2442-44-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-4-444-42220-2-2-2-222-2-2200-111-100006-600-3-3330000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-44444-4-444-42220-2-2-2-222-2-2200-111-10000-660033-3-30000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4-44-88444-4-8-4-4204-4-224-2-444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-444-4444-442220-22-22-2-22-2-243−43-11-1100−232300−23233−33−30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-444-4444-442220-22-22-2-22-2-2−4343-11-110023−230023−23−33−330000000000000000000000000000000000000000000000000000000

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