Finite Group Databasebeta

← Group #13167503

Character table — Group #13167503

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order1222344666336666661212121212123366666612121212121212121212444412121212224444448888121212121212121212122424242424242424661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ91-11-11i−i-11-1111-1-11-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−ii−i1-111-1-11-11-1i−ii−i1-1i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ101-11-11i−i-11-1111-1-11-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−ii−i1-111-1-11-1-11i−i−ii-11−iii−i-1-111−i−iii-1-111−i−iii1-1i−i
χ111-11-11i−i-11-1111-1-11-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−ii−i1-111-1-1-111-1−iii−i-11−iii−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ121-11-11i−i-11-1111-1-11-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−ii−i1-111-1-1-11-11−ii−ii1-1i−ii−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ131-11-11−ii-11-1111-1-11-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii−ii1-111-1-11-11-1−ii−ii1-1−ii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ141-11-11−ii-11-1111-1-11-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii−ii1-111-1-11-1-11−iii−i-11i−i−ii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ151-11-11−ii-11-1111-1-11-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii−ii1-111-1-1-111-1i−i−ii-11i−i−ii11-1-1−i−iii-1-111ii−i−i-11i−i
χ161-11-11−ii-11-1111-1-11-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii−ii1-111-1-1-11-11i−ii−i1-1−ii−ii-1-111ii−i−i11-1-1−i−iii-11i−i
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2000000000000-2-200000000000000000000
χ1822222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-20000000000002200000000000000000000
χ192222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1000000002222-1-100000000-1-1-1-1-1-1-1-10000
χ202222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-1-100000000111111110000
χ212222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2111100000000000011000000003−33−33−33−30000
χ222222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211110000000000001100000000−33−33−33−330000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-2-21111000000000000-1-1000000003−33−3−33−330000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-2-21111000000000000-1-100000000−33−333−33−30000
χ252222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-222-1-1-1-10000000022-2-21100000000-1-1-1-111110000
χ262222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-222-1-1-1-100000000-2-22211000000001111-1-1-1-10000
χ272-22-222i−2i-22-2222-2-22-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i−2i2i-22-2-222000000000000−2i2i00000000000000000000
χ282-22-22−2i2i-22-2222-2-22-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i2i−2i-22-2-2220000000000002i−2i00000000000000000000
χ292-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2i−2i2-2-1-111000000002-22i−2i−ii00000000-1-111−i−iii0000
χ302-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2i−2i2-2-1-11100000000-22−2i2i−ii0000000011-1-1ii−i−i0000
χ312-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii−2i2i-2211-1-1000000000000i−i000000003−3−33i3−i3−i3i30000
χ322-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii−2i2i-2211-1-1000000000000i−i00000000−333−3−i3i3i3−i30000
χ332-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2i−2i-2211-1-1000000000000−ii000000003−3−33−i3i3i3−i30000
χ342-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2i−2i-2211-1-1000000000000−ii00000000−333−3i3−i3−i3i30000
χ352-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i−2i2i2-2-1-111000000002-2−2i2ii−i00000000-1-111ii−i−i0000
χ362-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i−2i2i2-2-1-11100000000-222i−2ii−i0000000011-1-1−i−iii0000
χ3744444444441-2-21-211-24411111-21-21-21-2-2-211-2-211-2-20000000000220022000000-1-1-1-1-1-1-1-1000000000000
χ3844444444441-2-21-211-24411111-21-21-21-2-2-211-2-211-2-20000000000-2-200-2-200000011111111000000000000
χ394444444444-211-21-2-2144-2-2-2-2-21-21-21-2111-2-211-2-21100000000220022000000000000000000000000-1-1-1-1
χ404444444444-211-21-2-2144-2-2-2-2-21-21-21-2111-2-211-2-21100000000-2-200-2-20000000000000000000000001111
χ4144444-4-44441-2-21-211-2-4-4-1-1-1-11-21-21-21-222-1-122-1-12200000000002200-2-2000000-1-1-1-11111000000000000
χ4244444-4-44441-2-21-211-2-4-4-1-1-1-11-21-21-21-222-1-122-1-1220000000000-2-200220000001111-1-1-1-1000000000000
χ4344444-4-4444-211-21-2-21-4-42222-21-21-21-21-1-122-1-122-1-1000000002200-2-2000000000000000000000000-1-111
χ4444444-4-4444-211-21-2-21-4-42222-21-21-21-21-1-122-1-122-1-100000000-2-2002200000000000000000000000011-1-1
χ4544-4-44004-4-41-221-2-1-12003-33-31-2-12-121-2003-3003-30000000000000000000000003−33−33−33−3000000000000
χ4644-4-44004-4-41-221-2-1-12003-33-31-2-12-121-2003-3003-3000000000000000000000000−33−33−33−33000000000000
χ4744-4-44004-4-41-221-2-1-1200-33-331-2-12-121-200-3300-330000000000000000000000003−33−3−33−33000000000000
χ4844-4-44004-4-41-221-2-1-1200-33-331-2-12-121-200-3300-33000000000000000000000000−33−333−33−3000000000000
χ4944-4-44004-4-444-444-4-4-400000044-4-4-4-4440000000000000000000000000000000000000000000000000000
χ5044-4-4-200-22244-444-4-4-4000000-2-22222-2-20000000000000023−2323−230000000000000000000000000000000000
χ5144-4-4-200-22244-444-4-4-4000000-2-22222-2-200000000000000−2323−23230000000000000000000000000000000000
χ524-44-444i−4i-44-41-2-2-121-124i−4iii−i−i1-21-2-12-12−2i2iii−2i−2i−i−i2i2i00000000002-2002i−2i000000-1-111−i−iii000000000000
χ534-44-444i−4i-44-41-2-2-121-124i−4iii−i−i1-21-2-12-12−2i2iii−2i−2i−i−i2i2i0000000000-2200−2i2i00000011-1-1ii−i−i000000000000
χ544-44-444i−4i-44-4-2112-1-22-14i−4i−2i−2i2i2i-21-212-12-1i−i−2i−2iii2i2i−i−i000000002-2002i−2i000000000000000000000000-11−ii
χ554-44-444i−4i-44-4-2112-1-22-14i−4i−2i−2i2i2i-21-212-12-1i−i−2i−2iii2i2i−i−i00000000-2200−2i2i0000000000000000000000001-1i−i
χ564-44-44−4i4i-44-41-2-2-121-12−4i4i−i−iii1-21-2-12-122i−2i−i−i2i2iii−2i−2i00000000002-200−2i2i000000-1-111ii−i−i000000000000
χ574-44-44−4i4i-44-41-2-2-121-12−4i4i−i−iii1-21-2-12-122i−2i−i−i2i2iii−2i−2i0000000000-22002i−2i00000011-1-1−i−iii000000000000
χ584-44-44−4i4i-44-4-2112-1-22-1−4i4i2i2i−2i−2i-21-212-12-1−ii2i2i−i−i−2i−2iii000000002-200−2i2i000000000000000000000000-11i−i
χ594-44-44−4i4i-44-4-2112-1-22-1−4i4i2i2i−2i−2i-21-212-12-1−ii2i2i−i−i−2i−2iii00000000-22002i−2i0000000000000000000000001-1−ii
χ604-4-44400-4-441-22-12-11-2003i−3i−3i3i1-2-121-2-12003i−3i00−3i3i0000000000000000000000003−3−33i3−i3−i3i3000000000000
χ614-4-44400-4-441-22-12-11-2003i−3i−3i3i1-2-121-2-12003i−3i00−3i3i000000000000000000000000−333−3−i3i3i3−i3000000000000
χ624-4-44400-4-441-22-12-11-200−3i3i3i−3i1-2-121-2-1200−3i3i003i−3i0000000000000000000000003−3−33−i3i3i3−i3000000000000
χ634-4-44400-4-441-22-12-11-200−3i3i3i−3i1-2-121-2-1200−3i3i003i−3i000000000000000000000000−333−3i3−i3−i3i3000000000000
χ644-4-44400-4-4444-4-4-4-44400000044-4-444-4-40000000000000000000000000000000000000000000000000000
χ654-4-44-20022-244-4-4-4-444000000-2-222-2-2220000000000000023−23−23230000000000000000000000000000000000
χ664-4-44-20022-244-4-4-4-444000000-2-222-2-22200000000000000−232323−230000000000000000000000000000000000
χ678888-488-4-4-42-4-42-422-4-4-42222-12-12-12-12-4-4-1-122-1-122000000000000000000000000000000000000000000
χ688888-488-4-4-4-422-42-4-42-4-4-4-4-4-42-12-12-12-12222-1-122-1-1000000000000000000000000000000000000000000
χ698888-4-8-8-4-4-42-4-42-422-444-2-2-2-2-12-12-12-124411-2-211-2-2000000000000000000000000000000000000000000
χ708888-4-8-8-4-4-4-422-42-4-424444442-12-12-12-1-2-2-2-211-2-211000000000000000000000000000000000000000000
χ7188-8-88008-8-8-42-2-4244-2000000-424-24-2-420000000000000000000000000000000000000000000000000000
χ7288-8-8-400-4442-442-4-2-24006-66-6-121-21-2-1200-3300-3300000000000000000000000000000000000000000000
χ7388-8-8-400-4442-442-4-2-2400-66-66-121-21-2-12003-3003-300000000000000000000000000000000000000000000
χ7488-8-8-400-444-42-2-4244-20000002-1-21-212-10000−3i33i300−3i33i3000000000000000000000000000000000000000000
χ7588-8-8-400-444-42-2-4244-20000002-1-21-212-100003i3−3i3003i3−3i3000000000000000000000000000000000000000000
χ768-88-8-48i−8i4-442-4-4-242-24−4i4i2i2i−2i−2i-12-121-21-2−4i4i−i−i2i2iii−2i−2i000000000000000000000000000000000000000000
χ778-88-8-48i−8i4-44-4224-2-44-2−4i4i−4i−4i4i4i2-12-1-21-212i−2i2i2i−i−i−2i−2iii000000000000000000000000000000000000000000
χ788-88-8-4−8i8i4-442-4-4-242-244i−4i−2i−2i2i2i-12-121-21-24i−4iii−2i−2i−i−i2i2i000000000000000000000000000000000000000000
χ798-88-8-4−8i8i4-44-4224-2-44-24i−4i4i4i−4i−4i2-12-1-21-21−2i2i−2i−2iii2i2i−i−i000000000000000000000000000000000000000000
χ808-8-88800-8-88-42-24-24-42000000-424-2-424-20000000000000000000000000000000000000000000000000000
χ818-8-88-40044-42-44-24-22-4006i−6i−6i6i-121-2-121-200−3i3i003i−3i00000000000000000000000000000000000000000000
χ828-8-88-40044-42-44-24-22-400−6i6i6i−6i-121-2-121-2003i−3i00−3i3i00000000000000000000000000000000000000000000
χ838-8-88-40044-4-42-24-24-420000002-1-212-1-21000033−3300−3333000000000000000000000000000000000000000000
χ848-8-88-40044-4-42-24-24-420000002-1-212-1-210000−33330033−33000000000000000000000000000000000000000000

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