Finite Group Databasebeta

← Group #13165510

Character table — Group #13165510

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222333344444444888888881212121212121212121212121212121212121212181818181818242424242424242424242424363636363636363636363636363636363636545454545454
order122236664444336666663366666644441212121212121212121212121212121244888812121212121212121212121244441212121212121212121224242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111
χ511111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1
χ611111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-11-1-1-1-111111-1-1-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-1-1-11-1-1-1-1-1-11111
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−i111-1-1-11-1111-1-1-11-11-1i−iiiii−i−i−i−i11-1-1ii−i−i-11ii−i−ii−i1-111-1-1ii−i−i1-1i−i1ii−i−i11-1-1-1ii−i−ii−i11-1-1
χ101-11-11-1-11ii−i−i111-1-1-11-1111-1-1-11-11-1−iiiiii−i−i−i−i11-1-1−i−iii-11−i−iii−ii1-111-1-1−i−iii-11i−i1ii−i−i-1-111-1−i−iiii−i-1-111
χ111-11-11-1-11ii−i−i111-1-1-11-1111-1-1-11-1-11i−iiiii−i−i−i−i-1-111ii−i−i-11−i−iiii−i-11-1-111ii−i−i1-1−ii1−i−iii11-1-1-1−i−iiii−i-1-111
χ121-11-11-1-11ii−i−i111-1-1-11-1111-1-1-11-1-11−iiiiii−i−i−i−i-1-111−i−iii-11ii−i−i−ii-11-1-111−i−iii-11−ii1−i−iii-1-111-1ii−i−ii−i11-1-1
χ131-11-11-1-11−i−iii111-1-1-11-1111-1-1-11-11-1i−i−i−i−i−iiiii11-1-1ii−i−i-11ii−i−ii−i1-111-1-1ii−i−i-11−ii1−i−iii-1-111-1ii−i−i−ii-1-111
χ141-11-11-1-11−i−iii111-1-1-11-1111-1-1-11-11-1−ii−i−i−i−iiiii11-1-1−i−iii-11−i−iii−ii1-111-1-1−i−iii1-1−ii1−i−iii11-1-1-1−i−iii−ii11-1-1
χ151-11-11-1-11−i−iii111-1-1-11-1111-1-1-11-1-11i−i−i−i−i−iiiii-1-111ii−i−i-11−i−iiii−i-11-1-111ii−i−i-11i−i1ii−i−i-1-111-1−i−iii−ii11-1-1
χ161-11-11-1-11−i−iii111-1-1-11-1111-1-1-11-1-11−ii−i−i−i−iiiii-1-111−i−iii-11ii−i−i−ii-11-1-111−i−iii1-1i−i1ii−i−i11-1-1-1ii−i−i−ii-1-111
χ17222222222222222222222222222200002222222200000000-2-200000000000000000000-200000000-20000-2-20000
χ1822222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-200000000-2-200000000000000000000-200000000-20000220000
χ192222-1-1-1-1000022222222-1-1-1-1-1-1-1-122220000000022222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-100000000-1-1-1-1-1000000
χ202222-1-1-1-1000022222222-1-1-1-1-1-1-1-122-2-2000000002222-2-2-2-222-2-2-2-211-1-1-1-1-1-111110000-100000000-11111000000
χ212222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-22200000000-2-2-2-2222222-2-2-2-2-1-1111111-1-1-1-10000-100000000-11111000000
χ222222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2-2-2-2-2-2-22222221111111111110000-100000000-1-1-1-1-1000000
χ2322-2-222-2-22-22-222-222-2-2-222-222-2-2-2000022-2-222-2-200000000002−22−2000000000000000000000000002−22−2002−22−2
χ2422-2-222-2-22-22-222-222-2-2-222-222-2-2-2000022-2-222-2-20000000000−22−2200000000000000000000000000−22−2200−22−22
χ2522-2-222-2-2-22-2222-222-2-2-222-222-2-2-20000-2-222-2-22200000000002−22−2000000000000000000000000002−22−200−22−22
χ2622-2-222-2-2-22-2222-222-2-2-222-222-2-2-20000-2-222-2-2220000000000−22−2200000000000000000000000000−22−22002−22−2
χ272-22-22-2-222i2i−2i−2i222-2-2-22-2222-2-2-22-200002i2i2i2i−2i−2i−2i−2i000000002-200000000000000000000-20000000020000−2i2i0000
χ282-22-22-2-22−2i−2i2i2i222-2-2-22-2222-2-2-22-20000−2i−2i−2i−2i2i2i2i2i000000002-200000000000000000000-200000000200002i−2i0000
χ292-22-2-111-10000222-2-2-22-2-1-1-1111-112-22i−2i0000000022-2-22i2i−2i−2i-222i2i−2i−2i−ii-11-1-111−i−iii0000-1000000001−i−iii000000
χ302-22-2-111-10000222-2-2-22-2-1-1-1111-112-2−2i2i0000000022-2-2−2i−2i2i2i-22−2i−2i2i2ii−i-11-1-111ii−i−i0000-1000000001ii−i−i000000
χ312-22-2-111-10000222-2-2-22-2-1-1-1111-11-222i−2i00000000-2-2222i2i−2i−2i-22−2i−2i2i2i−ii1-111-1-1−i−iii0000-1000000001ii−i−i000000
χ322-22-2-111-10000222-2-2-22-2-1-1-1111-11-22−2i2i00000000-2-222−2i−2i2i2i-222i2i−2i−2ii−i1-111-1-1ii−i−i0000-1000000001−i−iii000000
χ332-2-222-22-22i−2i−2i2i22-2-2-22-2222-2-2-22-2200002i2i−2i−2i−2i−2i2i2i0000000000−i2i2i2−i200000000000000000000000000−i2i2i2−i200−222−2
χ342-2-222-22-22i−2i−2i2i22-2-2-22-2222-2-2-22-2200002i2i−2i−2i−2i−2i2i2i0000000000i2−i2−i2i200000000000000000000000000i2−i2−i2i2002−2−22
χ352-2-222-22-2−2i2i2i−2i22-2-2-22-2222-2-2-22-220000−2i−2i2i2i2i2i−2i−2i0000000000−i2i2i2−i200000000000000000000000000−i2i2i2−i2002−2−22
χ362-2-222-22-2−2i2i2i−2i22-2-2-22-2222-2-2-22-220000−2i−2i2i2i2i2i−2i−2i0000000000i2−i2−i2i200000000000000000000000000i2−i2−i2i200−222−2
χ374444444444441-211-2-2-211-2-21-211-222001-21-21-21-2-1-1-1-100000000000022-1-1-1-1000000220-1-1-1-1000000000000000
χ384444444444441-211-2-2-211-2-21-211-2-2-2001-21-21-21-21111000000000000-2-21111000000-2-201111000000000000000
χ39444444444444-21-2-2111-2-211-21-2-210022-21-21-21-210000-1-1-1-100000022000000-1-1-1-1220000000-1-1-1-100000000000
χ40444444444444-21-2-2111-2-211-21-2-2100-2-2-21-21-21-2100001111000000-2-20000001111-2-20000000111100000000000
χ4144444444-4-4-4-41-211-2-2-211-2-21-211-22200-12-12-12-12-1-1-1-100000000000022-1-1-1-1000000-2-201111000000000000000
χ4244444444-4-4-4-41-211-2-2-211-2-21-211-2-2-200-12-12-12-121111000000000000-2-21111000000220-1-1-1-1000000000000000
χ4344444444-4-4-4-4-21-2-2111-2-211-21-2-2100222-12-12-12-10000-1-1-1-100000022000000-1-1-1-1-2-20000000111100000000000
χ4444444444-4-4-4-4-21-2-2111-2-211-21-2-2100-2-22-12-12-12-100001111000000-2-20000001111220000000-1-1-1-100000000000
χ454444-2-2-2-2000044444444-2-2-2-2-2-2-2-200000000000000000000-4-40000000000000000000020000000020000000000
χ4644-4-444-4-44-44-41-2-11-222-11-221-2-1-1200001-2-121-2-123−33−3000000000000003−33−30000000003−33−3000000000000000
χ4744-4-444-4-44-44-41-2-11-222-11-221-2-1-1200001-2-121-2-12−33−3300000000000000−33−33000000000−33−33000000000000000
χ4844-4-444-4-44-44-4-212-21-1-12-21-1-2122-10000-212-1-212-100003−33−3000000000000003−33−30000000003−33−300000000000
χ4944-4-444-4-44-44-4-212-21-1-12-21-1-2122-10000-212-1-212-10000−33−3300000000000000−33−33000000000−33−3300000000000
χ5044-4-444-4-4-44-441-2-11-222-11-221-2-1-120000-121-2-121-23−33−3000000000000003−33−3000000000−33−33000000000000000
χ5144-4-444-4-4-44-441-2-11-222-11-221-2-1-120000-121-2-121-2−33−3300000000000000−33−330000000003−33−3000000000000000
χ5244-4-444-4-4-44-44-212-21-1-12-21-1-2122-100002-1-212-1-2100003−33−3000000000000003−33−3000000000−33−3300000000000
χ5344-4-444-4-4-44-44-212-21-1-12-21-1-2122-100002-1-212-1-210000−33−3300000000000000−33−330000000003−33−300000000000
χ5444-4-4-2-222000044-444-4-4-4-2-22-2-2222000000000000000000000022−2222−2200000000000000000000000000−22−22000000
χ5544-4-4-2-222000044-444-4-4-4-2-22-2-22220000000000000000000000−2222−2222000000000000000000000000002−22−2000000
χ564-44-44-4-444i4i−4i−4i1-21-122-2-11-2-2-12-1122-200i−2ii−2i−i2i−i2i-1-1110000000000002-2-1-1110000002i−2i0−i−iii000000000000000
χ574-44-44-4-444i4i−4i−4i1-21-122-2-11-2-2-12-112-2200i−2ii−2i−i2i−i2i11-1-1000000000000-2211-1-1000000−2i2i0ii−i−i000000000000000
χ584-44-44-4-444i4i−4i−4i-21-22-1-112-2112-12-2-1002i−2i−2ii−2ii2i−i2i−i0000−i−iii0000002i−2i000000−i−iii2-20000000-1-11100000000000
χ594-44-44-4-444i4i−4i−4i-21-22-1-112-2112-12-2-100−2i2i−2ii−2ii2i−i2i−i0000ii−i−i000000−2i2i000000ii−i−i-22000000011-1-100000000000
χ604-44-44-4-44−4i−4i4i4i1-21-122-2-11-2-2-12-1122-200−i2i−i2ii−2ii−2i-1-1110000000000002-2-1-111000000−2i2i0ii−i−i000000000000000
χ614-44-44-4-44−4i−4i4i4i1-21-122-2-11-2-2-12-112-2200−i2i−i2ii−2ii−2i11-1-1000000000000-2211-1-10000002i−2i0−i−iii000000000000000
χ624-44-44-4-44−4i−4i4i4i-21-22-1-112-2112-12-2-1002i−2i2i−i2i−i−2ii−2ii0000−i−iii0000002i−2i000000−i−iii-22000000011-1-100000000000
χ634-44-44-4-44−4i−4i4i4i-21-22-1-112-2112-12-2-100−2i2i2i−i2i−i−2ii−2ii0000ii−i−i000000−2i2i000000ii−i−i2-20000000-1-11100000000000
χ644-44-4-222-20000444-4-4-44-4-2-2-2222-22000000000000000000004-400000000000000000000200000000-20000000000
χ654-4-444-44-44i−4i−4i4i1-2-1-12-2211-22-121-1-20000i−2i−i2i−i2ii−2i3−3−33000000000000003−3−33000000000i3−i3−i3i3000000000000000
χ664-4-444-44-44i−4i−4i4i1-2-1-12-2211-22-121-1-20000i−2i−i2i−i2ii−2i−333−300000000000000−333−3000000000−i3i3i3−i3000000000000000
χ674-4-444-44-44i−4i−4i4i-2122-11-1-2-21-12-1-2210000−2ii2i−i2i−i−2ii0000−i3i3i3−i300000000000000−i3i3i3−i3000000000−333−300000000000
χ684-4-444-44-44i−4i−4i4i-2122-11-1-2-21-12-1-2210000−2ii2i−i2i−i−2ii0000i3−i3−i3i300000000000000i3−i3−i3i30000000003−3−3300000000000
χ694-4-444-44-4−4i4i4i−4i1-2-1-12-2211-22-121-1-20000−i2ii−2ii−2i−i2i3−3−33000000000000003−3−33000000000−i3i3i3−i3000000000000000
χ704-4-444-44-4−4i4i4i−4i1-2-1-12-2211-22-121-1-20000−i2ii−2ii−2i−i2i−333−300000000000000−333−3000000000i3−i3−i3i3000000000000000
χ714-4-444-44-4−4i4i4i−4i-2122-11-1-2-21-12-1-22100002i−i−2ii−2ii2i−i0000−i3i3i3−i300000000000000−i3i3i3−i30000000003−3−3300000000000
χ724-4-444-44-4−4i4i4i−4i-2122-11-1-2-21-12-1-22100002i−i−2ii−2ii2i−i0000i3−i3−i3i300000000000000i3−i3−i3i3000000000−333−300000000000
χ734-4-44-22-22000044-4-4-44-44-2-2222-22-20000000000000000000000−2i22i22i2−2i200000000000000000000000000i2−i2−i2i2000000
χ744-4-44-22-22000044-4-4-44-44-2-2222-22-200000000000000000000002i2−2i2−2i22i200000000000000000000000000−i2i2i2−i2000000
χ758888-4-4-4-400002-422-4-4-42-122-12-1-12440000000000-2-2-2-2000000000000-2-211110000000000000000000000000000
χ768888-4-4-4-400002-422-4-4-42-122-12-1-12-4-40000000000222200000000000022-1-1-1-10000000000000000000000000000
χ778888-4-4-4-40000-42-4-4222-42-1-12-122-10044000000000000-2-2-2-2000000-2-20000001111000000000000000000000000
χ788888-4-4-4-40000-42-4-4222-42-1-12-122-100-4-4000000000000222200000022000000-1-1-1-1000000000000000000000000
χ7988-8-8-4-44400002-4-22-444-2-12-2-1211-200000000000023−2323−2300000000000000−33−330000000000000000000000000000
χ8088-8-8-4-44400002-4-22-444-2-12-2-1211-2000000000000−2323−2323000000000000003−33−30000000000000000000000000000
χ8188-8-8-4-4440000-424-42-2-242-112-1-2-21000000000000000023−2323−2300000000000000−33−33000000000000000000000000
χ8288-8-8-4-4440000-424-42-2-242-112-1-2-210000000000000000−2323−2323000000000000003−33−3000000000000000000000000
χ838-88-8-444-400002-42-244-4-2-1221-21-1-24-40000000000-2-222000000000000-2211-1-10000000000000000000000000000
χ848-88-8-444-400002-42-244-4-2-1221-21-1-2-44000000000022-2-20000000000002-2-1-1110000000000000000000000000000
χ858-88-8-444-40000-42-44-2-2242-1-1-21-221004i−4i000000000000−2i−2i2i2i000000−2i2i000000ii−i−i000000000000000000000000
χ868-88-8-444-40000-42-44-2-2242-1-1-21-22100−4i4i0000000000002i2i−2i−2i0000002i−2i000000−i−iii000000000000000000000000
χ878-8-88-44-4400002-4-2-24-442-12-21-2-11200000000000023−23−232300000000000000−333−30000000000000000000000000000
χ888-8-88-44-4400002-4-2-24-442-12-21-2-112000000000000−232323−23000000000000003−3−330000000000000000000000000000
χ898-8-88-44-440000-4244-22-2-42-11-212-2-10000000000000000−2i32i32i3−2i300000000000000i3−i3−i3i3000000000000000000000000
χ908-8-88-44-440000-4244-22-2-42-11-212-2-100000000000000002i3−2i3−2i32i300000000000000−i3i3i3−i3000000000000000000000000

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