Finite Group Databasebeta

← Group #13167511

Character table — Group #13167511

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222244444444444444888888888888888888181818181818363636363636363636363636363636363636363636363636363636727272727272
order1222344666336666661212121212123366666612121212121212121212441212121244444888812121212121212121212242424242424242424661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-2-2-2-200000000-2-20000000000000000000000
χ1022222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2200000000220000000000000000000000
χ112222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1200002222-1-100000000-1-1-1-1-1-1-1-1000000
χ122222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-120000-2-2-2-2-1-10000000011111111000000
χ132222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-200000000110000000033−3−333−3−3000000
χ142222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2000000001100000000−3−333−3−333000000
χ152222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-2000022-2-21100000000-1-1-1-11111000000
χ162222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-20000-2-22211000000001111-1-1-1-1000000
χ172222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-21111200000000-1-10000000033−3−3−3−333000000
χ182222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-21111200000000-1-100000000−3−33333−3−3000000
χ192-22-222i−2i-22-2222-2-22-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i000000000002−2−i2i200000000002−22−2−i2i2−i2i2000000
χ202-22-222i−2i-22-2222-2-22-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i00000000000−22i2−i20000000000−22−22i2−i2i2−i2000000
χ212-22-22−2i2i-22-2222-2-22-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i000000000002−2i2−i200000000002−22−2i2−i2i2−i2000000
χ222-22-22−2i2i-22-2222-2-22-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i00000000000−22−i2i20000000000−22−22−i2i2−i2i2000000
χ232-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii003−33−3000002−2−i2i2−i3i300000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ242-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii003−33−300000−22i2−i2−i3i300000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ252-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii00−33−33000002−2−i2i2i3−i300000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ262-22-2-12i−2i1-11222-2-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii00−33−3300000−22i2−i2i3−i300000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ272-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i003−33−3000002−2i2−i2i3−i300000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ282-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i003−33−300000−22−i2i2i3−i300000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ292-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i00−33−33000002−2i2−i2−i3i300000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ302-22-2-1−2i2i1-11222-2-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i00−33−3300000−22−i2i2−i3i300000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ312-2-22200-2-2222-2-2-2-22200000022-2-222-2-200000000002-222-2-202i−2i000000002i2i−2i−2i000000000000000000
χ322-2-22200-2-2222-2-2-2-22200000022-2-222-2-200000000002-222-2-20−2i2i00000000−2i−2i2i2i000000000000000000
χ332-2-22200-2-2222-2-2-2-22200000022-2-222-2-20000000000-22-2-2220002-2000000000022-2-200000000000000
χ342-2-22200-2-2222-2-2-2-22200000022-2-222-2-20000000000-22-2-222000-220000000000-2-22200000000000000
χ3544444444441-2-21-211-24411111-21-21-21-2-2-211-2-211-2-200000002222000000-1-1-1-1-1-1-1-100000000000000
χ3644444444441-2-21-211-24411111-21-21-21-2-2-211-2-211-2-20000000-2-2-2-20000001111111100000000000000
χ374444444444-211-21-2-2144-2-2-2-2-21-21-21-2111-2-211-2-21100000000000000000000000000000000022-1-1-1-1
χ384444444444-211-21-2-2144-2-2-2-2-21-21-21-2111-2-211-2-211000000000000000000000000000000000-2-21111
χ3944444-4-44441-2-21-211-2-4-4-1-1-1-11-21-21-21-222-1-122-1-122000000022-2-2000000-1-1-1-1111100000000000000
χ4044444-4-44441-2-21-211-2-4-4-1-1-1-11-21-21-21-222-1-122-1-1220000000-2-2220000001111-1-1-1-100000000000000
χ4144444-4-4444-211-21-2-21-4-42222-21-21-21-21-1-122-1-122-1-10000000000000000000000000000000002-2-1-111
χ4244444-4-4444-211-21-2-21-4-42222-21-21-21-21-1-122-1-122-1-1000000000000000000000000000000000-2211-1-1
χ4344-4-44004-4-41-221-2-1-12003-33-31-2-12-121-2003-3003-300000000000000000003−33−33−33−300000000000000
χ4444-4-44004-4-41-221-2-1-12003-33-31-2-12-121-2003-3003-30000000000000000000−33−33−33−3300000000000000
χ4544-4-44004-4-41-221-2-1-1200-33-331-2-12-121-200-3300-3300000000000000000003−33−3−33−3300000000000000
χ4644-4-44004-4-41-221-2-1-1200-33-331-2-12-121-200-3300-330000000000000000000−33−333−33−300000000000000
χ4744-4-44004-4-444-444-4-4-400000044-4-4-4-4440000000000000000000000000000000000000000000000000
χ4844-4-4-200-22244-444-4-4-4000000-2-22222-2-200000000000023−23−2323000000000000000000000000000000000
χ4944-4-4-200-22244-444-4-4-4000000-2-22222-2-2000000000000−232323−23000000000000000000000000000000000
χ504-44-444i−4i-44-41-2-2-121-124i−4iii−i−i1-21-2-12-12−2i2iii−2i−2i−i−i2i2i00000000000000000−i3i3i3−i33−3−3300000000000000
χ514-44-444i−4i-44-41-2-2-121-124i−4iii−i−i1-21-2-12-12−2i2iii−2i−2i−i−i2i2i00000000000000000i3−i3−i3i3−333−300000000000000
χ524-44-444i−4i-44-4-2112-1-22-14i−4i−2i−2i2i2i-21-212-12-1i−i−2i−2iii2i2i−i−i00000000000000000000000000000000000−i3i33−3
χ534-44-444i−4i-44-4-2112-1-22-14i−4i−2i−2i2i2i-21-212-12-1i−i−2i−2iii2i2i−i−i00000000000000000000000000000000000i3−i3−33
χ544-44-44−4i4i-44-41-2-2-121-12−4i4i−i−iii1-21-2-12-122i−2i−i−i2i2iii−2i−2i00000000000000000−i3i3i3−i3−333−300000000000000
χ554-44-44−4i4i-44-41-2-2-121-12−4i4i−i−iii1-21-2-12-122i−2i−i−i2i2iii−2i−2i00000000000000000i3−i3−i3i33−3−3300000000000000
χ564-44-44−4i4i-44-4-2112-1-22-1−4i4i2i2i−2i−2i-21-212-12-1−ii2i2i−i−i−2i−2iii00000000000000000000000000000000000−i3i3−33
χ574-44-44−4i4i-44-4-2112-1-22-1−4i4i2i2i−2i−2i-21-212-12-1−ii2i2i−i−i−2i−2iii00000000000000000000000000000000000i3−i33−3
χ584-4-44400-4-441-22-12-11-2003i−3i−3i3i1-2-121-2-12003i−3i00−3i3i0000000002i−2i-22000000−i−iii11-1-100000000000000
χ594-4-44400-4-441-22-12-11-2003i−3i−3i3i1-2-121-2-12003i−3i00−3i3i000000000−2i2i2-2000000ii−i−i-1-11100000000000000
χ604-4-44400-4-441-22-12-11-200−3i3i3i−3i1-2-121-2-1200−3i3i003i−3i0000000002i−2i2-2000000−i−iii-1-11100000000000000
χ614-4-44400-4-441-22-12-11-200−3i3i3i−3i1-2-121-2-1200−3i3i003i−3i000000000−2i2i-22000000ii−i−i11-1-100000000000000
χ624-4-44-20022-244-4-4-4-444000000-2-222-2-22200000000004-4-2-222000000000000000000000000000000000
χ634-4-44-20022-244-4-4-4-444000000-2-222-2-2220000000000-4422-2-2000000000000000000000000000000000
χ648888-488-4-4-42-4-42-422-4-4-42222-12-12-12-12-4-4-1-122-1-122000000000000000000000000000000000000000
χ658888-488-4-4-4-422-42-4-42-4-4-4-4-4-42-12-12-12-12222-1-122-1-1000000000000000000000000000000000000000
χ668888-4-8-8-4-4-42-4-42-422-444-2-2-2-2-12-12-12-124411-2-211-2-2000000000000000000000000000000000000000
χ678888-4-8-8-4-4-4-422-42-4-424444442-12-12-12-1-2-2-2-211-2-211000000000000000000000000000000000000000
χ6888-8-88008-8-8-42-2-4244-2000000-424-24-2-420000000000000000000000000000000000000000000000000
χ6988-8-8-400-4442-442-4-2-24006-66-6-121-21-2-1200-3300-3300000000000000000000000000000000000000000
χ7088-8-8-400-4442-442-4-2-2400-66-66-121-21-2-12003-3003-300000000000000000000000000000000000000000
χ7188-8-8-400-444-42-2-4244-20000002-1-21-212-10000−3i33i300−3i33i3000000000000000000000000000000000000000
χ7288-8-8-400-444-42-2-4244-20000002-1-21-212-100003i3−3i3003i3−3i3000000000000000000000000000000000000000
χ738-88-8-48i−8i4-442-4-4-242-24−4i4i2i2i−2i−2i-12-121-21-2−4i4i−i−i2i2iii−2i−2i000000000000000000000000000000000000000
χ748-88-8-48i−8i4-44-4224-2-44-2−4i4i−4i−4i4i4i2-12-1-21-212i−2i2i2i−i−i−2i−2iii000000000000000000000000000000000000000
χ758-88-8-4−8i8i4-442-4-4-242-244i−4i−2i−2i2i2i-12-121-21-24i−4iii−2i−2i−i−i2i2i000000000000000000000000000000000000000
χ768-88-8-4−8i8i4-44-4224-2-44-24i−4i4i4i−4i−4i2-12-1-21-21−2i2i−2i−2iii2i2i−i−i000000000000000000000000000000000000000
χ778-8-88800-8-88-42-24-24-42000000-424-2-424-20000000000000000000000000000000000000000000000000
χ788-8-88-40044-42-44-24-22-4006i−6i−6i6i-121-2-121-200−3i3i003i−3i00000000000000000000000000000000000000000
χ798-8-88-40044-42-44-24-22-400−6i6i6i−6i-121-2-121-2003i−3i00−3i3i00000000000000000000000000000000000000000
χ808-8-88-40044-4-42-24-24-420000002-1-212-1-21000033−3300−3333000000000000000000000000000000000000000
χ818-8-88-40044-4-42-24-24-420000002-1-212-1-210000−33330033−33000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.