Finite Group Databasebeta

← Group #13165503

Character table — Group #13165503

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222333344444444888888881212121212121212121212121212121212121212181818181818242424242424242424242424363636363636363636363636363636363636545454545454
order12223666444433666666336666664444121212121212121212121212121212124488881212121212121212121212122244666612121212121224242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-111-1-111111-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111111
χ511111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1
χ611111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111111-1-1-1-11-1-1-1-1-1-11111
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ91-11-11-1-11ii−i−i111-1-1-1-111111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-111-1-1i−ii−iii−i−iii−i−i1-11-111-1-1-111-1-1111-1-1i−iii−i−i
χ101-11-11-1-11ii−i−i111-1-1-1-111111-1-1-1-1i−i−iiii−i−i−i−iiiii−i−iii−i−i1-1-1-111i−i−iiii−i−i−i−iii1-1-1111-1-1-1-1-1111-1-111i−i−i−iii
χ111-11-11-1-11ii−i−i111-1-1-1-111111-1-1-1-1−iii−iii−i−iii−i−iii−i−i−i−iii1-1-1-111−iii−i−i−iiiii−i−i-111-1-1-111-111-1-11-1-111i−i−i−iii
χ121-11-11-1-11ii−i−i111-1-1-1-111111-1-1-1-1−ii−iiii−i−i−i−iiiii−i−i−i−iii1-111-1-1−ii−ii−i−iii−i−iii-11-11-1-111-1-1-111111-1-1i−iii−i−i
χ131-11-11-1-11−i−iii111-1-1-1-111111-1-1-1-1i−ii−i−i−iiiii−i−i−i−iiiii−i−i1-111-1-1i−ii−iii−i−iii−i−i-11-11-1-111-1-1-111111-1-1−ii−i−iii
χ141-11-11-1-11−i−iii111-1-1-1-111111-1-1-1-1i−i−ii−i−iii−i−iii−i−iiiii−i−i1-1-1-111i−i−iiii−i−i−i−iii-111-1-1-111-111-1-11-1-111−iiii−i−i
χ151-11-11-1-11−i−iii111-1-1-1-111111-1-1-1-1−iii−i−i−iiiii−i−i−i−iii−i−iii1-1-1-111−iii−i−i−iiiii−i−i1-1-1111-1-1-1-1-1111-1-111−iiii−i−i
χ161-11-11-1-11−i−iii111-1-1-1-111111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-111-1-1−ii−ii−i−iii−i−iii1-11-111-1-1-111-1-1111-1-1−ii−i−iii
χ17222222222222222222222222222200002222000022220000-2-2000000000000000000000000-20000-20000-2-20000
χ1822222222-2-2-2-222222222222222220000-2-2-2-20000-2-2-2-20000-2-2000000000000000000000000-20000-20000220000
χ192222-1-1-1-1000022222222-1-1-1-1-1-1-1-122220000222200002222222222-1-1-1-1-1-1-1-1-1-1-1-100000000-10000-1-1-1-1-1000000
χ202222-1-1-1-1000022222222-1-1-1-1-1-1-1-122-2-20000-2-2-2-20000222222-2-2-2-2-1-111-1-1-1-1111100000000-10000-11111000000
χ212222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-222000022220000-2-2-2-222-2-2-2-211-1-11111-1-1-1-100000000-10000-11111000000
χ222222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-20000-2-2-2-222222211111111111100000000-10000-1-1-1-1-1000000
χ2322-2-222-2-22-22-222-2-22-22-222-2-22-22-200002-22-200002-22-2000000−i2i2−i2i200000000000000000000000000−i2i2−i2i200−i2i2−i2i2
χ2422-2-222-2-22-22-222-2-22-22-222-2-22-22-200002-22-200002-22-2000000i2−i2i2−i200000000000000000000000000i2−i2i2−i200i2−i2i2−i2
χ2522-2-222-2-2-22-2222-2-22-22-222-2-22-22-20000-22-220000-22-22000000−i2i2−i2i200000000000000000000000000−i2i2−i2i200i2−i2i2−i2
χ2622-2-222-2-2-22-2222-2-22-22-222-2-22-22-20000-22-220000-22-22000000i2−i2i2−i200000000000000000000000000i2−i2i2−i200−i2i2−i2i2
χ272-22-22-2-222i2i−2i−2i222-2-2-2-222222-2-2-2-200002i2i−2i−2i00002i2i−2i−2i0000-2200000000000000000000000020000-20000−2i2i0000
χ282-22-22-2-22−2i−2i2i2i222-2-2-2-222222-2-2-2-20000−2i−2i2i2i0000−2i−2i2i2i0000-2200000000000000000000000020000-200002i−2i0000
χ292-22-2-111-10000222-2-2-2-22-1-1-1-111112i−2i2i−2i00002i2i−2i−2i00002i2i−2i−2i2-222-2-2−ii−ii−i−iii−i−iii0000000010000-1-1-111000000
χ302-22-2-111-10000222-2-2-2-22-1-1-1-111112i−2i−2i2i0000−2i−2i2i2i00002i2i−2i−2i2-2-2-222−iii−i−i−iiiii−i−i0000000010000-111-1-1000000
χ312-22-2-111-10000222-2-2-2-22-1-1-1-11111−2i2i2i−2i00002i2i−2i−2i0000−2i−2i2i2i2-2-2-222i−i−iiii−i−i−i−iii0000000010000-111-1-1000000
χ322-22-2-111-10000222-2-2-2-22-1-1-1-11111−2i2i−2i2i0000−2i−2i2i2i0000−2i−2i2i2i2-222-2-2i−ii−iii−i−iii−i−i0000000010000-1-1-111000000
χ332-2-222-22-22i−2i−2i2i22-22-22-2-222-2-2-22-2200002i−2i−2i2i00002i−2i−2i2i000000−i2i2i2−i200000000000000000000000000−i2i2i2−i2002−2−22
χ342-2-222-22-22i−2i−2i2i22-22-22-2-222-2-2-22-2200002i−2i−2i2i00002i−2i−2i2i000000i2−i2−i2i200000000000000000000000000i2−i2−i2i200−222−2
χ352-2-222-22-2−2i2i2i−2i22-22-22-2-222-2-2-22-220000−2i2i2i−2i0000−2i2i2i−2i000000−i2i2i2−i200000000000000000000000000−i2i2i2−i200−222−2
χ362-2-222-22-2−2i2i2i−2i22-22-22-2-222-2-2-22-220000−2i2i2i−2i0000−2i2i2i−2i000000i2−i2−i2i200000000000000000000000000i2−i2−i2i2002−2−22
χ374444444444441-2-2-211-211-21-21-2-2100221111-1-1-1-1-2-2-2-2000000000000220000-1-1-1-1002200000-1-1-1-100000000000
χ384444444444441-2-2-211-211-21-21-2-2100-2-211111111-2-2-2-2000000000000-2-20000111100-2-200000111100000000000
χ39444444444444-2111-2-21-2-21-21-211-22200-2-2-2-200001111-1-1-1-10000002200-1-1-1-100002200-1-1-1-10000000000000000
χ40444444444444-2111-2-21-2-21-21-211-2-2-200-2-2-2-2000011111111000000-2-20011110000-2-20011110000000000000000
χ4144444444-4-4-4-41-2-2-211-211-21-21-2-210022-1-1-1-1-1-1-1-12222000000000000220000-1-1-1-100-2-200000111100000000000
χ4244444444-4-4-4-41-2-2-211-211-21-21-2-2100-2-2-1-1-1-111112222000000000000-2-200001111002200000-1-1-1-100000000000
χ4344444444-4-4-4-4-2111-2-21-2-21-21-211-2220022220000-1-1-1-1-1-1-1-10000002200-1-1-1-10000-2-20011110000000000000000
χ4444444444-4-4-4-4-2111-2-21-2-21-21-211-2-2-20022220000-1-1-1-11111000000-2-200111100002200-1-1-1-10000000000000000
χ454444-2-2-2-2000044444444-2-2-2-2-2-2-2-200000000000000000000-4-40000000000000000000000002000020000000000
χ4644-4-444-4-44-44-41-2221-1-2-11-2-1212-2-100001-11-13−33−3-22-220000000000000000003−33−30000000003−33−300000000000
χ4744-4-444-4-44-44-41-2221-1-2-11-2-1212-2-100001-11-1−33−33-22-22000000000000000000−33−33000000000−33−3300000000000
χ4844-4-444-4-44-44-4-21-1-1-2212-212-1-2-1120000-22-2200001-11-1−i3i3−i3i30000000000−i3i3−i3i300000000−i3i3−i3i30000000000000000
χ4944-4-444-4-44-44-4-21-1-1-2212-212-1-2-1120000-22-2200001-11-1i3−i3i3−i30000000000i3−i3i3−i300000000i3−i3i3−i30000000000000000
χ5044-4-444-4-4-44-441-2221-1-2-11-2-1212-2-10000-11-113−33−32-22-20000000000000000003−33−3000000000−33−3300000000000
χ5144-4-444-4-4-44-441-2221-1-2-11-2-1212-2-10000-11-11−33−332-22-2000000000000000000−33−330000000003−33−300000000000
χ5244-4-444-4-4-44-44-21-1-1-2212-212-1-2-11200002-22-20000-11-11−i3i3−i3i30000000000−i3i3−i3i300000000i3−i3i3−i30000000000000000
χ5344-4-444-4-4-44-44-21-1-1-2212-212-1-2-11200002-22-20000-11-11i3−i3i3−i30000000000i3−i3i3−i300000000−i3i3−i3i30000000000000000
χ5444-4-4-2-222000044-4-44-44-4-2-222-22-220000000000000000000000−2i22i2−2i22i200000000000000000000000000i2−i2i2−i2000000
χ5544-4-4-2-222000044-4-44-44-4-2-222-22-2200000000000000000000002i2−2i22i2−2i200000000000000000000000000−i2i2−i2i2000000
χ564-44-44-4-444i4i−4i−4i1-2-22-1-1211-21-2-122-1002i−2iii−i−i−i−iii−2i−2i2i2i0000000000002i−2i0000−i−iii002-200000-1-11100000000000
χ574-44-44-4-444i4i−4i−4i1-2-22-1-1211-21-2-122-100−2i2iii−i−iii−i−i−2i−2i2i2i000000000000−2i2i0000ii−i−i00-220000011-1-100000000000
χ584-44-44-4-444i4i−4i−4i-211-122-1-2-21-212-1-122i−2i00−2i−2i2i2i0000ii−i−i−i−iii0000002i−2i00−i−iii00002-200-1-1110000000000000000
χ594-44-44-4-444i4i−4i−4i-211-122-1-2-21-212-1-12−2i2i00−2i−2i2i2i0000ii−i−iii−i−i000000−2i2i00ii−i−i0000-220011-1-10000000000000000
χ604-44-44-4-44−4i−4i4i4i1-2-22-1-1211-21-2-122-1002i−2i−i−iii−i−iii2i2i−2i−2i0000000000002i−2i0000−i−iii00-220000011-1-100000000000
χ614-44-44-4-44−4i−4i4i4i1-2-22-1-1211-21-2-122-100−2i2i−i−iiiii−i−i2i2i−2i−2i000000000000−2i2i0000ii−i−i002-200000-1-11100000000000
χ624-44-44-4-44−4i−4i4i4i-211-122-1-2-21-212-1-122i−2i002i2i−2i−2i0000−i−iii−i−iii0000002i−2i00−i−iii0000-220011-1-10000000000000000
χ634-44-44-4-44−4i−4i4i4i-211-122-1-2-21-212-1-12−2i2i002i2i−2i−2i0000−i−iiiii−i−i000000−2i2i00ii−i−i00002-200-1-1110000000000000000
χ644-44-4-222-20000444-4-4-4-44-2-2-2-2222200000000000000000000-44000000000000000000000000-2000020000000000
χ654-4-444-44-44i−4i−4i4i1-22-2-112-11-2-12-1-2210000i−i−ii−i3i3i3−i3−2i2i2i−2i000000000000000000−i3i3i3−i3000000000−333−300000000000
χ664-4-444-44-44i−4i−4i4i1-22-2-112-11-2-12-1-2210000i−i−iii3−i3−i3i3−2i2i2i−2i000000000000000000i3−i3−i3i30000000003−3−3300000000000
χ674-4-444-44-44i−4i−4i4i-21-112-2-12-212-121-1-20000−2i2i2i−2i0000i−i−ii3−3−3300000000003−3−3300000000−i3i3i3−i30000000000000000
χ684-4-444-44-44i−4i−4i4i-21-112-2-12-212-121-1-20000−2i2i2i−2i0000i−i−ii−333−30000000000−333−300000000i3−i3−i3i30000000000000000
χ694-4-444-44-4−4i4i4i−4i1-22-2-112-11-2-12-1-2210000−iii−i−i3i3i3−i32i−2i−2i2i000000000000000000−i3i3i3−i30000000003−3−3300000000000
χ704-4-444-44-4−4i4i4i−4i1-22-2-112-11-2-12-1-2210000−iii−ii3−i3−i3i32i−2i−2i2i000000000000000000i3−i3−i3i3000000000−333−300000000000
χ714-4-444-44-4−4i4i4i−4i-21-112-2-12-212-121-1-200002i−2i−2i2i0000−iii−i3−3−3300000000003−3−3300000000i3−i3−i3i30000000000000000
χ724-4-444-44-4−4i4i4i−4i-21-112-2-12-212-121-1-200002i−2i−2i2i0000−iii−i−333−30000000000−333−300000000−i3i3i3−i30000000000000000
χ734-4-44-22-22000044-44-44-4-4-2-2222-22-20000000000000000000000−2i22i22i2−2i200000000000000000000000000i2−i2−i2i2000000
χ744-4-44-22-22000044-44-44-4-4-2-2222-22-200000000000000000000002i2−2i2−2i22i200000000000000000000000000−i2i2i2−i2000000
χ758888-4-4-4-400002-4-4-422-42-12-12-122-100440000-2-2-2-20000000000000000-2-200001111000000000000000000000000
χ768888-4-4-4-400002-4-4-422-42-12-12-122-100-4-4000022220000000000000000220000-1-1-1-1000000000000000000000000
χ778888-4-4-4-40000-4222-4-42-42-12-12-1-124400000000000000-2-2-2-2000000-2-20011110000000000000000000000000000
χ788888-4-4-4-40000-4222-4-42-42-12-12-1-12-4-40000000000000022220000002200-1-1-1-10000000000000000000000000000
χ7988-8-8-4-44400002-4442-2-4-2-121-2-1-2210000000023−2323−230000000000000000000000−33−33000000000000000000000000
χ8088-8-8-4-44400002-4442-2-4-2-121-2-1-22100000000−2323−232300000000000000000000003−33−3000000000000000000000000
χ8188-8-8-4-4440000-42-2-2-44242-1-2121-1-20000000000000000−2i32i3−2i32i30000000000i3−i3i3−i30000000000000000000000000000
χ8288-8-8-4-4440000-42-2-2-44242-1-2121-1-200000000000000002i3−2i32i3−2i30000000000−i3i3−i3i30000000000000000000000000000
χ838-88-8-444-400002-4-44-2-242-12-121-2-21004i−4i0000−2i−2i2i2i0000000000000000−2i2i0000ii−i−i000000000000000000000000
χ848-88-8-444-400002-4-44-2-242-12-121-2-2100−4i4i00002i2i−2i−2i00000000000000002i−2i0000−i−iii000000000000000000000000
χ858-88-8-444-40000-422-244-2-42-12-1-211-24i−4i00000000000000−2i−2i2i2i000000−2i2i00ii−i−i0000000000000000000000000000
χ868-88-8-444-40000-422-244-2-42-12-1-211-2−4i4i000000000000002i2i−2i−2i0000002i−2i00−i−iii0000000000000000000000000000
χ878-8-88-44-4400002-44-4-224-2-121-212-2-100000000−2i32i32i3−2i30000000000000000000000i3−i3−i3i3000000000000000000000000
χ888-8-88-44-4400002-44-4-224-2-121-212-2-1000000002i3−2i3−2i32i30000000000000000000000−i3i3i3−i3000000000000000000000000
χ898-8-88-44-440000-42-224-4-242-1-21-2-112000000000000000023−23−23230000000000−333−30000000000000000000000000000
χ908-8-88-44-440000-42-224-4-242-1-21-2-1120000000000000000−232323−2300000000003−3−330000000000000000000000000000

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