Finite Group Databasebeta

← Group #13168122

Character table — Group #13168122

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612123666121212121212121212121212222444666666121222444466666666612121212121212121212122446612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-11111111111-1-11-111-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-1111111-1-111-1-111-1-1-111-1-11111-111-11-1-111111-1-1-1-111-1-1-1-11-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-111
χ511111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111111111111-11-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-11-1-111-1-1-1-11-1-11-111-1-1-1-11-1-1-1-111-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1111-1-1-1-1-1-1-1111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-111-1-11111-1-111-1-11-111111-1-1-1-1-1-11-1-111-1-1-111-1-11111-1-1-111-1
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111-1-111-1-1-1-1-1-1111-111111-1-1-111-1-1-1-1-1-1111-11-1-1-1-1-1-11111-11
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-1-1-111111111-1-11-1-111-1-11-1-1111111-1-1-1-1-11111-1-111-1-1-11
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-11111-111-1-11111-111-1-111-1-11-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111111111-1-1-1-111-111-1-111-1-1-1-11-1-111-1-111-111-1-111-1-11-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11111-1-111111111-111-1-111-111-1-1-1-1-1-111-1-1-11111-1-111-1-11-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1-1-1-111-11-1-1-1-1-1111-1-1111111-1-11-11-1-1-1-1-1-111111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111-1-1-1-1-1-111-1-1-11-1-1-1-1-1111111-111-1-111-111-1-11111-1-1-11-11
χ17222222-12-1-122-12222-1-122-1-1-1-1-12-1222-1-1-1-1-12-1-1-1-122-1-1-1-122220022-1-1-1-10022000022-1-1-1-1-1-1-1-10020-1-10000002-1-10000000-100
χ18222222-12-1-122-12222-1-122-1-1-1-1-12-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-2-20022-1-11100-2-20000-22-111-1-1-1-1100-2011000000-2110000000100
χ19222222-12-1-122-12222-1-122-1-1-1-1-12-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-22200-2-211-1-100-2-200002-21-1-11111-10020-1-1000000-2110000000100
χ20222222-12-1-122-12222-1-122-1-1-1-1-12-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-2-200-2-2111100220000-2-21111111100-20110000002-1-10000000-100
χ21222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-11-21111-2-211112-22-2002211-1-100-2-200002-2-1-1-1-1-111100-20110000002110000000-100
χ22222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-11-21111-2-211112-2-220022111100220000-2-2-111-1-111-10020-1-1000000-2-1-10000000100
χ23222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-11-21111-2-21111-222-200-2-2-1-1-1-100220000221-1-111-1-1100-2011000000-2-1-10000000100
χ24222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-2-1-1-1-11-21111-2-21111-22-2200-2-2-1-11100-2-20000-2211111-1-1-10020-1-10000002110000000-100
χ2522222-12-1222-1222-1-12-12-12-1-12-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-1220022-1-12200-1-10022000-1200-1-1-1-102-10200-1-1-1-120000-1-10000-1000
χ2622222-12-1222-1222-1-12-12-12-1-12-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-12200-2-2-1-122001100-2-2000-1200-1-1-1-10-210-2001111-200001100001000
χ2722222-12-1222-1222-1-12-12-12-1-12-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2002211-2-200-1-100-2-20001-200111102-10200-1-1-1-1-200001100001000
χ2822222-12-1222-1222-1-12-12-12-1-12-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-200-2-211-2-2001100220001-20011110-210-200111120000-1-10000-1000
χ2922222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-21-2-2111111112-2002-2-1-1-2-200-1-100220001200-1-1110-210200-1-111-20000-1-100001000
χ3022222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-21-2-2111111112-200-22-1-1-2-2001100-2-20001200-1-11102-10-20011-1-120000110000-1000
χ3122222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-21-2-211111111-22002-2112200-1-100-2-2000-1-20011-1-10-210200-1-11120000110000-1000
χ3222222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-21-2-211111111-2200-22112200110022000-1-20011-1-102-10-20011-1-1-20000-1-100001000
χ332222-122222-122-1-12-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100222200002222000022-100-1-100002-12-1-1-1-1-1-1-1-10200000-1-1-1-10000
χ342222-122222-122-1-12-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10022-2-2000022-2-20000-2-2-100-1-1000021-2-11-1-111110-20000011110000
χ352222-122222-122-1-12-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100-2-2220000-2-2220000-2-2100110000-2-121-111-1-1-1-10-20000011110000
χ362222-122222-122-1-12-1-122-1-122-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100-2-2-2-20000-2-2-2-2000022100110000-21-2111111110200000-1-1-1-10000
χ372222-122222-122-1-12-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-2111111002-22-2000022220000-2-2-100-1-10000-21-21-111-1-1110200000-1-1110000
χ382222-122222-122-1-12-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-2111111002-2-22000022-2-2000022-100-1-10000-2-12111111-1-10-20000011-1-10000
χ392222-122222-122-1-12-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-211111100-222-20000-2-22200002210011000021-2-1-1-1-1-1-1110-20000011-1-10000
χ402222-122222-122-1-12-1-12-2-1-122-12-1-1-111-1-1-1-1-2-211-2-211111100-22-220000-2-2-2-20000-2-21001100002-12-11-1-111-1-10200000-1-1110000
χ4122-2-22222-22-2-2-22-2-222202-22-2-2-2-22-20022-2-2000000000000000000000000002-22i−2i2i−2i000000000000000000000002-22i−2i002i−2i0000
χ4222-2-22222-22-2-2-22-2-222202-22-2-2-2-22-20022-2-2000000000000000000000000002-2−2i2i−2i2i000000000000000000000002-2−2i2i00−2i2i0000
χ4322-2-22222-22-2-2-22-2-222202-22-2-2-2-22-20022-2-200000000000000000000000000-222i−2i−2i2i00000000000000000000000-222i−2i00−2i2i0000
χ4422-2-22222-22-2-2-22-2-222202-22-2-2-2-22-20022-2-200000000000000000000000000-22−2i2i2i−2i00000000000000000000000-22−2i2i002i−2i0000
χ4544444-2-2-2-2-24-2-244-2-2-214-2-211-21-2-2-2441111-2-2-2-211-2-21111440000-2-2-2-200000000000-2-200111100000000000000000000000000
χ4644444-2-2-2-2-24-2-244-2-2-214-2-211-21-2-2-2441111-2-2-2-211-2-21111-4-400002222000000000002200-1-1-1-100000000000000000000000000
χ4744444-2-2-2-2-24-2-244-2-2-21-4-2-211-21-2-2-2-4-411112222-1-122-1-1-1-14-40000-2-222000000000002-20011-1-100000000000000000000000000
χ4844444-2-2-2-2-24-2-244-2-2-21-4-2-211-21-2-2-2-4-411112222-1-122-1-1-1-1-44000022-2-200000000000-2200-1-11100000000000000000000000000
χ494444-24-24-2-2-24-2-2-24-21-24-21-2-21-2-21-2-2-21111-2411-2-2-2-211110044000000-2-200000000-200110000-200-20110000000000000000000
χ504444-24-24-2-2-24-2-2-24-21-24-21-2-21-2-21-2-2-21111-2411-2-2-2-2111100-4-40000002200000000200-1-1000020020-1-10000000000000000000
χ514444-24-24-2-2-24-2-2-24-21-2-4-21-2-21-2-21-22211112-4-1-12222-1-1-1-1004-4000000-2-200000000-20011000020020-1-10000000000000000000
χ524444-24-24-2-2-24-2-2-24-21-2-4-21-2-21-2-21-22211112-4-1-12222-1-1-1-100-440000002200000000200-1-10000-200-20110000000000000000000
χ534444-2-24-244-2-24-2-2-21-2-241-2-2-2-2-21-21-2-211114-2-2-2-2-2111111000044000000-2-20000000000000000-2-20-2001111000000000000000
χ544444-2-24-244-2-24-2-2-21-2-241-2-2-2-2-21-21-2-211114-2-2-2-2-21111110000-4-4000000220000000000000000220200-1-1-1-1000000000000000
χ554444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-2-21-21221111-422222-1-1-1-1-1-100004-4000000-2-20000000000000000220-20011-1-1000000000000000
χ564444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-2-21-21221111-422222-1-1-1-1-1-10000-44000000220000000000000000-2-20200-1-111000000000000000
χ5744-4-444-242-2-4-424-4-44-2-2042-2222-4-2-400-2-222000000000000000000000000004-4000000000000000000000000000-220000000000
χ5844-4-444-242-2-4-424-4-44-2-2042-2222-4-2-400-2-22200000000000000000000000000-440000000000000000000000000002-20000000000
χ5944-4-44-24-2-44-42-44-42-24-20-2-4-22-4224200-2-22200000000000000000000000000004i−4i000000000000000000000000000−2i2i00000000
χ6044-4-44-24-2-44-42-44-42-24-20-2-4-22-4224200-2-2220000000000000000000000000000−4i4i0000000000000000000000000002i−2i00000000
χ6144-4-4-2444-442-4-4-22-4-2-240-224-42-42-2200-2-2220000000000000000000000000000004i−4i00000000000000000000000000000−2i2i0000
χ6244-4-4-2444-442-4-4-22-4-2-240-224-42-42-2200-2-222000000000000000000000000000000−4i4i000000000000000000000000000002i−2i0000
χ634-44-4444-4-4-4-4-44-4444440-44-44-4-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-2-422-4-4-2-4444-2-20-4-22-22242-400-22-220000000000000000000000−2i32i300000000000−2i32i3000000000000000000000000000000
χ654-44-444-2-422-4-4-2-4444-2-20-4-22-22242-400-22-2200000000000000000000002i3−2i3000000000002i3−2i3000000000000000000000000000000
χ664-44-44-242-4-4-424-44-2-24-20242-2-42-2-4200-22-22000000000000000000000000−2i32i30000000000000000000000−2i32i300000000000000000
χ674-44-44-242-4-4-424-44-2-24-20242-2-42-2-4200-22-220000000000000000000000002i3−2i300000000000000000000002i3−2i300000000000000000
χ684-44-4-244-4-4-42-442-24-2-2402-2-442-4-22223−23-22-220023−230023−232323−23−230000000000000000000000000000000000000000000000000000000
χ694-44-4-244-4-4-42-442-24-2-2402-2-442-4-222−2323-22-2200−232300−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ704-44-4-24-2-4222-4-22-24-21-20212-2-12-2-1223−231-11-100−330023−23−3−3330000000000−2i32i300000000000i3−i30000000003i−3i0000000000000000000
χ714-44-4-24-2-4222-4-22-24-21-20212-2-12-2-1223−231-11-100−330023−23−3−33300000000002i3−2i300000000000−i3i3000000000−3i3i0000000000000000000
χ724-44-4-24-2-4222-4-22-24-21-20212-2-12-2-12−23231-11-1003−300−232333−3−30000000000−2i32i300000000000i3−i3000000000−3i3i0000000000000000000
χ734-44-4-24-2-4222-4-22-24-21-20212-2-12-2-12−23231-11-1003−300−232333−3−300000000002i3−2i300000000000−i3i30000000003i−3i0000000000000000000
χ744-44-4-2-242-4-42242-2-21-2-20-1-22-22212-123−231-11-10023−2300−33−3−333000000000000−2i32i30000000000000000000000i3−i33i−3i000000000000000
χ754-44-4-2-242-4-42242-2-21-2-20-1-22-22212-123−231-11-10023−2300−33−3−3330000000000002i3−2i30000000000000000000000−i3i3−3i3i000000000000000
χ764-44-4-2-242-4-42242-2-21-2-20-1-22-22212-1−23231-11-100−2323003−333−3−3000000000000−2i32i30000000000000000000000i3−i3−3i3i000000000000000
χ774-44-4-2-242-4-42242-2-21-2-20-1-22-22212-1−23231-11-100−2323003−333−3−30000000000002i3−2i30000000000000000000000−i3i33i−3i000000000000000
χ784-4-44444-44-444-4-4-4-44440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-22442-4-4-44-2-20-4222-2-2-42400-222-200000000000000000000−2i32i300000000000000000−2i32i300000000000000000000000000
χ804-4-4444-2-4-22442-4-4-44-2-20-4222-2-2-42400-222-2000000000000000000002i3−2i3000000000000000002i3−2i300000000000000000000000000
χ814-4-444-2424-44-2-4-4-42-24-202-4224-22-4-200-222-2000000000000000000−2i32i300000000000000000−2i32i30000000000000000000000000000
χ824-4-444-2424-44-2-4-4-42-24-202-4224-22-4-200-222-20000000000000000002i3−2i3000000000000000002i3−2i30000000000000000000000000000
χ834-4-444-2-22-224-22-4-42-2-21022-1-1-2122-2001-1-1100003-3003-33-3000000−2i32i3−2i32i3000000000000000i3−i3i3−i300000000000000000000000000
χ844-4-444-2-22-224-22-4-42-2-21022-1-1-2122-2001-1-1100003-3003-33-30000002i3−2i32i3−2i3000000000000000−i3i3−i3i300000000000000000000000000
χ854-4-444-2-22-224-22-4-42-2-21022-1-1-2122-2001-1-110000-3300-33-33000000−2i32i32i3−2i3000000000000000i3−i3−i3i300000000000000000000000000
χ864-4-444-2-22-224-22-4-42-2-21022-1-1-2122-2001-1-110000-3300-33-330000002i3−2i3−2i32i3000000000000000−i3i3i3−i300000000000000000000000000
χ874-4-44-244-44-4-24-422-4-2-24022-4-4-2422-200-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ884-4-44-244-44-4-24-422-4-2-24022-4-4-2422-200-222-200000000000000000000000000000000000000000000000000000000000−2323000000
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
χ9188-8-88-4-4-44-4-8448-84-4-420-442-24-24-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-484-44-84-44-8-42-40-4-2-44-244240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-4-8844-8-4442-4-4024-4444-2-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-4444-44422202-22-2-2-2-22-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-44-4444-44422202-22-2-2-2-22-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ968-88-88-4-4444-84-4-88-4-4-4204-4-224-2-444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444444-44-4-42220-22-22-2-22-2-243−43-11-1100−232300−232333−3−30000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444444-44-4-42220-22-22-2-22-2-2−4343-11-110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-8-44-48444-8-42-404-2442-44-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4848-8-4-4-84442-4-40-2444-4-4-242002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44-4-444442220-2-2-2-222-2-2200-111-100006-600-33-330000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44-4-444442220-2-2-2-222-2-2200-111-10000-66003-33-30000000000000000000000000000000000000000000000000000000

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