Finite Group Databasebeta

← Group #13165494

Character table — Group #13165494

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222333344444444888888881212121212121212121212121212121212121212181818181818242424242424242424242424363636363636363636363636363636363636545454545454
order1222366644443366666633666666444412121212121212121212121212121212448888121212121212121212121212222266666666121224242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ511111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ611111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-11111
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
χ911-1-11-11-1ii−i−i1111-1-1-1-11111-1-1-1-1i−ii−iiiii−i−i−i−iii−i−iii−i−i1-111-1-1i−ii−iii−i−iii−i−i1-11-111-1-111-1-1-1111-1-1i−iii−i−i
χ1011-1-11-11-1ii−i−i1111-1-1-1-11111-1-1-1-1i−i−iiiiii−i−i−i−iii−i−i−i−iii1-1-1-111i−i−iiii−i−i−i−iii1-1-1111-1-1-1-111-11-1-111i−i−i−iii
χ1111-1-11-11-1ii−i−i1111-1-1-1-11111-1-1-1-1−iii−iiiii−i−i−i−i−i−iiiii−i−i1-1-1-111−iii−i−i−iiiii−i−i-111-1-1-11111-1-1-11-1-111i−i−i−iii
χ1211-1-11-11-1ii−i−i1111-1-1-1-11111-1-1-1-1−ii−iiiiii−i−i−i−i−i−iii−i−iii1-111-1-1−ii−ii−i−iii−i−iii-11-11-1-111-1-111-1111-1-1i−iii−i−i
χ1311-1-11-11-1−i−iii1111-1-1-1-11111-1-1-1-1i−ii−i−i−i−i−iiiiiii−i−iii−i−i1-111-1-1i−ii−iii−i−iii−i−i-11-11-1-111-1-111-1111-1-1−ii−i−iii
χ1411-1-11-11-1−i−iii1111-1-1-1-11111-1-1-1-1i−i−ii−i−i−i−iiiiiii−i−i−i−iii1-1-1-111i−i−iiii−i−i−i−iii-111-1-1-11111-1-1-11-1-111−iiii−i−i
χ1511-1-11-11-1−i−iii1111-1-1-1-11111-1-1-1-1−iii−i−i−i−i−iiiii−i−iiiii−i−i1-1-1-111−iii−i−i−iiiii−i−i1-1-1111-1-1-1-111-11-1-111−iiii−i−i
χ1611-1-11-11-1−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii−i−i−i−iiiii−i−iii−i−iii1-111-1-1−ii−ii−i−iii−i−iii1-11-111-1-111-1-1-1111-1-1−ii−i−iii
χ17222222222222222222222222222200002222222200000000-2-20000000000000000000000000000-2-20000-2-20000
χ1822222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-200000000-2-20000000000000000000000000000-2-20000220000
χ192222-1-1-1-1000022222222-1-1-1-1-1-1-1-122220000000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1000000
χ202222-1-1-1-1000022222222-1-1-1-1-1-1-1-122-2-2000000002222-2-2-2-222-2-2-2-2-1-111-1-1-1-11111000000000000-1-11111000000
χ212222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-22200000000-2-2-2-2222222-2-2-2-211-1-11111-1-1-1-1000000000000-1-11111000000
χ222222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2-2-2-2-2-2-2222222111111111111000000000000-1-1-1-1-1-1000000
χ2322-2-22-22-22i2i−2i−2i2222-2-2-2-22222-2-2-2-200002i2i2i2i−2i−2i−2i−2i00000000-2200000000000000000000000000002-20000−2i2i0000
χ2422-2-22-22-2−2i−2i2i2i2222-2-2-2-22222-2-2-2-20000−2i−2i−2i−2i2i2i2i2i00000000-2200000000000000000000000000002-200002i−2i0000
χ2522-2-2-11-1100002222-2-2-2-2-1-1-1-111112i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i2-222-2-2−ii−ii−i−iii−i−iii0000000000001-1-1-111000000
χ2622-2-2-11-1100002222-2-2-2-2-1-1-1-111112i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i2-2-2-222−iii−i−i−iiiii−i−i0000000000001-111-1-1000000
χ2722-2-2-11-1100002222-2-2-2-2-1-1-1-11111−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i2-2-2-222i−i−iiii−i−i−i−iii0000000000001-111-1-1000000
χ2822-2-2-11-1100002222-2-2-2-2-1-1-1-11111−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-222-2-2i−ii−iii−i−iii−i−i0000000000001-1-1-111000000
χ292-22-22-2-222-22-222-2-2-2-22222-2-2-2-222000022-2-222-2-200000000002−22−2000000000000000000000000002−22−2002−22−2
χ302-22-22-2-222-22-222-2-2-2-22222-2-2-2-222000022-2-222-2-20000000000−22−2200000000000000000000000000−22−2200−22−22
χ312-22-22-2-22-22-2222-2-2-2-22222-2-2-2-2220000-2-222-2-22200000000002−22−2000000000000000000000000002−22−200−22−22
χ322-22-22-2-22-22-2222-2-2-2-22222-2-2-2-2220000-2-222-2-2220000000000−22−2200000000000000000000000000−22−22002−22−2
χ332-2-2222-2-22i−2i−2i2i22-2-222-2-222-2-222-2-200002i2i−2i−2i−2i−2i2i2i00000000002−2−22000000000000000000000000002−2−2200i2−i2−i2i2
χ342-2-2222-2-22i−2i−2i2i22-2-222-2-222-2-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000−222−200000000000000000000000000−222−200−i2i2i2−i2
χ352-2-2222-2-2−2i2i2i−2i22-2-222-2-222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i00000000002−2−22000000000000000000000000002−2−2200−i2i2i2−i2
χ362-2-2222-2-2−2i2i2i−2i22-2-222-2-222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000−222−200000000000000000000000000−222−200i2−i2−i2i2
χ374444444444441-21-21-21-21-21-21-21-200221-21-21-21-20000-1-1-1-100000000220000-1-1-1-100220000-1-1-1-1000000000000
χ384444444444441-21-21-21-21-21-21-21-200-2-21-21-21-21-20000111100000000-2-20000111100-2-200001111000000000000
χ39444444444444-21-21-21-21-21-21-21-212200-21-21-21-21-1-1-1-100000000002200-1-1-1-100002200-1-1-1-10000000000000000
χ40444444444444-21-21-21-21-21-21-21-21-2-200-21-21-21-2111110000000000-2-20011110000-2-20011110000000000000000
χ4144444444-4-4-4-41-21-21-21-21-21-21-21-20022-12-12-12-120000-1-1-1-100000000220000-1-1-1-100-2-200001111000000000000
χ4244444444-4-4-4-41-21-21-21-21-21-21-21-200-2-2-12-12-12-120000111100000000-2-20000111100220000-1-1-1-1000000000000
χ4344444444-4-4-4-4-21-21-21-21-21-21-21-2122002-12-12-12-1-1-1-1-100000000002200-1-1-1-10000-2-20011110000000000000000
χ4444444444-4-4-4-4-21-21-21-21-21-21-21-21-2-2002-12-12-12-111110000000000-2-200111100002200-1-1-1-10000000000000000
χ454444-2-2-2-2000044444444-2-2-2-2-2-2-2-200000000000000000000-4-40000000000000000000000000000220000000000
χ4644-4-44-44-44i4i−4i−4i1-21-2-12-121-21-2-12-12002i−2ii−2ii−2i−i2i−i2i0000−i−iii000000002i−2i0000−i−iii002-20000-1-111000000000000
χ4744-4-44-44-44i4i−4i−4i1-21-2-12-121-21-2-12-1200−2i2ii−2ii−2i−i2i−i2i0000ii−i−i00000000−2i2i0000ii−i−i00-22000011-1-1000000000000
χ4844-4-44-44-44i4i−4i−4i-21-212-12-1-21-212-12-12i−2i00−2ii−2ii2i−i2i−i−i−iii00000000002i−2i00−i−iii00002-200-1-1110000000000000000
χ4944-4-44-44-44i4i−4i−4i-21-212-12-1-21-212-12-1−2i2i00−2ii−2ii2i−i2i−iii−i−i0000000000−2i2i00ii−i−i0000-220011-1-10000000000000000
χ5044-4-44-44-4−4i−4i4i4i1-21-2-12-121-21-2-12-12002i−2i−i2i−i2ii−2ii−2i0000−i−iii000000002i−2i0000−i−iii00-22000011-1-1000000000000
χ5144-4-44-44-4−4i−4i4i4i1-21-2-12-121-21-2-12-1200−2i2i−i2i−i2ii−2ii−2i0000ii−i−i00000000−2i2i0000ii−i−i002-20000-1-111000000000000
χ5244-4-44-44-4−4i−4i4i4i-21-212-12-1-21-212-12-12i−2i002i−i2i−i−2ii−2ii−i−iii00000000002i−2i00−i−iii0000-220011-1-10000000000000000
χ5344-4-44-44-4−4i−4i4i4i-21-212-12-1-21-212-12-1−2i2i002i−i2i−i−2ii−2iiii−i−i0000000000−2i2i00ii−i−i00002-200-1-1110000000000000000
χ5444-4-4-22-2200004444-4-4-4-4-2-2-2-2222200000000000000000000-440000000000000000000000000000-220000000000
χ554-44-44-4-444-44-41-2-12-121-21-2-12-121-200001-2-121-2-120000−i3i3−i3i300000000000000−i3i3−i3i300000000−i3i3−i3i3000000000000
χ564-44-44-4-444-44-41-2-12-121-21-2-12-121-200001-2-121-2-120000i3−i3i3−i300000000000000i3−i3i3−i300000000i3−i3i3−i3000000000000
χ574-44-44-4-444-44-4-212-12-1-21-212-12-1-210000-212-1-212-1−i3i3−i3i300000000000000−i3i3−i3i300000000−i3i3−i3i30000000000000000
χ584-44-44-4-444-44-4-212-12-1-21-212-12-1-210000-212-1-212-1i3−i3i3−i300000000000000i3−i3i3−i300000000i3−i3i3−i30000000000000000
χ594-44-44-4-44-44-441-2-12-121-21-2-12-121-20000-121-2-121-20000−i3i3−i3i300000000000000−i3i3−i3i300000000i3−i3i3−i3000000000000
χ604-44-44-4-44-44-441-2-12-121-21-2-12-121-20000-121-2-121-20000i3−i3i3−i300000000000000i3−i3i3−i300000000−i3i3−i3i3000000000000
χ614-44-44-4-44-44-44-212-12-1-21-212-12-1-2100002-1-212-1-21−i3i3−i3i300000000000000−i3i3−i3i300000000i3−i3i3−i30000000000000000
χ624-44-44-4-44-44-44-212-12-1-21-212-12-1-2100002-1-212-1-21i3−i3i3−i300000000000000i3−i3i3−i300000000−i3i3−i3i30000000000000000
χ634-44-4-222-2000044-4-4-4-444-2-22222-2-2000000000000000000000022−2222−2200000000000000000000000000−22−22000000
χ644-44-4-222-2000044-4-4-4-444-2-22222-2-20000000000000000000000−2222−2222000000000000000000000000002−22−2000000
χ654-4-4444-4-44i−4i−4i4i1-2-121-2-121-2-121-2-120000i−2i−i2i−i2ii−2i00003−3−33000000000000003−3−3300000000−i3i3i3−i3000000000000
χ664-4-4444-4-44i−4i−4i4i1-2-121-2-121-2-121-2-120000i−2i−i2i−i2ii−2i0000−333−300000000000000−333−300000000i3−i3−i3i3000000000000
χ674-4-4444-4-44i−4i−4i4i-212-1-212-1-212-1-212-10000−2ii2i−i2i−i−2ii3−3−33000000000000003−3−3300000000−i3i3i3−i30000000000000000
χ684-4-4444-4-44i−4i−4i4i-212-1-212-1-212-1-212-10000−2ii2i−i2i−i−2ii−333−300000000000000−333−300000000i3−i3−i3i30000000000000000
χ694-4-4444-4-4−4i4i4i−4i1-2-121-2-121-2-121-2-120000−i2ii−2ii−2i−i2i00003−3−33000000000000003−3−3300000000i3−i3−i3i3000000000000
χ704-4-4444-4-4−4i4i4i−4i1-2-121-2-121-2-121-2-120000−i2ii−2ii−2i−i2i0000−333−300000000000000−333−300000000−i3i3i3−i3000000000000
χ714-4-4444-4-4−4i4i4i−4i-212-1-212-1-212-1-212-100002i−i−2ii−2ii2i−i3−3−33000000000000003−3−3300000000i3−i3−i3i30000000000000000
χ724-4-4444-4-4−4i4i4i−4i-212-1-212-1-212-1-212-100002i−i−2ii−2ii2i−i−333−300000000000000−333−300000000−i3i3i3−i30000000000000000
χ734-4-44-2-222000044-4-444-4-4-2-222-2-222000000000000000000000022−22−222200000000000000000000000000−222−2000000
χ744-4-44-2-222000044-4-444-4-4-2-222-2-2220000000000000000000000−222222−22000000000000000000000000002−2−22000000
χ758888-4-4-4-400002-42-42-42-4-12-12-12-120044000000000000-2-2-2-200000000-2-200001111000000000000000000000000
χ768888-4-4-4-400002-42-42-42-4-12-12-12-1200-4-4000000000000222200000000220000-1-1-1-1000000000000000000000000
χ778888-4-4-4-40000-42-42-42-422-12-12-12-1440000000000-2-2-2-20000000000-2-20011110000000000000000000000000000
χ788888-4-4-4-40000-42-42-42-422-12-12-12-1-4-40000000000222200000000002200-1-1-1-10000000000000000000000000000
χ7988-8-8-44-4400002-42-4-24-24-12-121-21-2004i−4i000000000000−2i−2i2i2i00000000−2i2i0000ii−i−i000000000000000000000000
χ8088-8-8-44-4400002-42-4-24-24-12-121-21-200−4i4i0000000000002i2i−2i−2i000000002i−2i0000−i−iii000000000000000000000000
χ8188-8-8-44-440000-42-424-24-22-12-1-21-214i−4i0000000000−2i−2i2i2i0000000000−2i2i00ii−i−i0000000000000000000000000000
χ8288-8-8-44-440000-42-424-24-22-12-1-21-21−4i4i00000000002i2i−2i−2i00000000002i−2i00−i−iii0000000000000000000000000000
χ838-88-8-444-400002-4-24-242-4-121-21-2-120000000000000000−2i32i3−2i32i300000000000000i3−i3i3−i3000000000000000000000000
χ848-88-8-444-400002-4-24-242-4-121-21-2-1200000000000000002i3−2i32i3−2i300000000000000−i3i3−i3i3000000000000000000000000
χ858-88-8-444-40000-424-24-2-422-1-21-212-1000000000000−2i32i3−2i32i300000000000000i3−i3i3−i30000000000000000000000000000
χ868-88-8-444-40000-424-24-2-422-1-21-212-10000000000002i3−2i32i3−2i300000000000000−i3i3−i3i30000000000000000000000000000
χ878-8-88-4-44400002-4-242-4-24-121-2-121-2000000000000000023−23−232300000000000000−333−3000000000000000000000000
χ888-8-88-4-44400002-4-242-4-24-121-2-121-20000000000000000−232323−23000000000000003−3−33000000000000000000000000
χ898-8-88-4-4440000-424-2-424-22-1-212-1-2100000000000023−23−232300000000000000−333−30000000000000000000000000000
χ908-8-88-4-4440000-424-2-424-22-1-212-1-21000000000000−232323−23000000000000003−3−330000000000000000000000000000

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