Finite Group Databasebeta

← Group #13166313

Character table — Group #13166313

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444444466888888888888888888889999121818181818181818242424242424242436363636363636363636363636545454545454108108108
order12223666334666666121244336666661212121212121212121212124444288881212121266661212121248812122424242424242424448888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-1
χ311111111111111111111111111111111111111111-1-1-1-11ii−i−i-1-1-1-111111111-1i−i-1-1iiii−i−i−i−i-1-1ii−i−i-1i−i
χ411111111111111111111111111111111111111111-1-1-1-11−i−iii-1-1-1-111111111-1−ii-1-1−i−i−i−iiiii-1-1−i−iii-1−ii
χ51111111111111111111-1-1111111111111111111111111-111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-11111-111
χ71111111111111111111-1-111111111111111111111-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1i−i-1-1iiii−i−i−i−i11−i−iii1−ii
χ81111111111111111111-1-111111111111111111111-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1−ii-1-1−i−i−i−iiiii11ii−i−i1i−i
χ91111111111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-11111-1-1-1-1-111-1-111-1-1111111-1-1-1
χ101111111111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1-111
χ111111111111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-111111−ii11ii−i−i−i−iii-1-1ii−i−i1−ii
χ121111111111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-111111i−i11−i−iiiii−i−i-1-1−i−iii1i−i
χ131111111111-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111
χ141111111111-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-111-1-1-1-111-1-111-1-111111-1-1
χ151111111111-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i-1-1-1-11111-1-1-1-11−ii11ii−i−i−i−iii11−i−iii-1i−i
χ161111111111-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iii-1-1-1-11111-1-1-1-11i−i11−i−iiiii−i−i11ii−i−i-1−ii
χ172222-1-1-1-1222222222-1-100-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222202222-1-1-1-100000000222-1-1-1-1-1-1-1-1-1-1000000000
χ182222-1-1-1-1222222222-1-100-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220-2-2-2-2-1-1-1-1000000002-2-2-1-111111111000000000
χ192222-1-1-1-1222222222-1-100-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-202i2i−2i−2i111100000000-22i−2i11−i−i−i−iiiii000000000
χ202222-1-1-1-1222222222-1-100-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20−2i−2i2i2i111100000000-2−2i2i11iiii−i−i−i−i000000000
χ212222-1-1-1-122-22222221100-1-1-1-1-1-1-1-1-2-2-2-211111111222202222-1-1-1-100000000-2-2-211-1-111-1-111000000000
χ222222-1-1-1-122-22222221100-1-1-1-1-1-1-1-1-2-2-2-21111111122220-2-2-2-2-1-1-1-100000000-2221111-1-111-1-1000000000
χ232222-1-1-1-122-22222221100-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-202i2i−2i−2i1111000000002−2i2i-1-1−i−iiiii−i−i000000000
χ242222-1-1-1-122-22222221100-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-20−2i−2i2i2i11110000000022i−2i-1-1ii−i−i−i−iii000000000
χ2522-2-22-22-2220-2-2-2-22200002222-2-2-2-20000000000002i−2i2i−2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i00000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000
χ2622-2-22-22-2220-2-2-2-22200002222-2-2-2-20000000000002i−2i2i−2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i0000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000
χ2722-2-22-22-2220-2-2-2-22200002222-2-2-2-2000000000000−2i2i−2i2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i0000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000
χ2822-2-22-22-2220-2-2-2-22200002222-2-2-2-2000000000000−2i2i−2i2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i00000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000
χ2922-2-2-11-11220-2-2-2-2223−300-1-1-1-1111100003333−3−3−3−32i−2i2i−2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ii−ii00000000000−i3i3−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000
χ3022-2-2-11-11220-2-2-2-2223−300-1-1-1-1111100003333−3−3−3−32i−2i2i−2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−ii−ii00000000000−i3i3ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000
χ3122-2-2-11-11220-2-2-2-2223−300-1-1-1-1111100003333−3−3−3−3−2i2i−2i2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−ii−i00000000000i3−i3ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000
χ3222-2-2-11-11220-2-2-2-2223−300-1-1-1-1111100003333−3−3−3−3−2i2i−2i2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−ii−i00000000000i3−i3−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000
χ3322-2-2-11-11220-2-2-2-222−3300-1-1-1-111110000−3−3−3−333332i−2i2i−2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ii−ii00000000000i3−i3−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000
χ3422-2-2-11-11220-2-2-2-222−3300-1-1-1-111110000−3−3−3−333332i−2i2i−2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−ii−ii00000000000i3−i3ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000
χ3522-2-2-11-11220-2-2-2-222−3300-1-1-1-111110000−3−3−3−33333−2i2i−2i2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−ii−i00000000000−i3i3ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000
χ3622-2-2-11-11220-2-2-2-222−3300-1-1-1-111110000−3−3−3−33333−2i2i−2i2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−ii−i00000000000−i3i3−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000
χ372-22-222-2-2220-2-222-2-2000022-2-2-2-2220000000000002i−2i−2i2i00000−2i2i2i−2i00000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000
χ382-22-222-2-2220-2-222-2-2000022-2-2-2-2220000000000002i−2i−2i2i00000−2i2i2i−2i000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000
χ392-22-222-2-2220-2-222-2-2000022-2-2-2-222000000000000−2i2i2i−2i000002i−2i−2i2i000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000
χ402-22-222-2-2220-2-222-2-2000022-2-2-2-222000000000000−2i2i2i−2i000002i−2i−2i2i00000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000
χ412-2-222-2-2222022-2-2-2-2002i−2i22-2-222-2-200000000000022-2-200000-2-22200002i2i−2i−2i00000000000002i−2i0000000
χ422-2-222-2-2222022-2-2-2-2002i−2i22-2-222-2-2000000000000-2-2220000022-2-200002i2i−2i−2i0000000000000−2i2i0000000
χ432-2-222-2-2222022-2-2-2-200−2i2i22-2-222-2-200000000000022-2-200000-2-2220000−2i−2i2i2i0000000000000−2i2i0000000
χ442-2-222-2-2222022-2-2-2-200−2i2i22-2-222-2-2000000000000-2-2220000022-2-20000−2i−2i2i2i00000000000002i−2i0000000
χ45444444441-241-21-21-244441-21-21-21-211-2-211-2-211-2-2000040000000011-2-21-21-20000000000000000000000
χ46444444441-241-21-21-244-4-41-21-21-21-211-2-211-2-211-2-20000-400000000-1-122-12-120000000000000000000000
χ47444444441-2-41-21-21-2-4-4441-21-21-21-2-1-122-1-122-1-1220000-400000000-1-1221-21-20000000000000000000000
χ48444444441-2-41-21-21-2-4-4-4-41-21-21-21-2-1-122-1-122-1-122000040000000011-2-2-12-120000000000000000000000
χ4944444444-214-21-21-214444-21-21-21-21-2-211-2-211-2-2110000400000000-2-211-21-210000000000000000000000
χ5044444444-214-21-21-2144-4-4-21-21-21-21-2-211-2-211-2-2110000-40000000022-1-12-12-10000000000000000000000
χ5144444444-21-4-21-21-21-4-444-21-21-21-2122-1-122-1-122-1-10000-40000000022-1-1-21-210000000000000000000000
χ5244444444-21-4-21-21-21-4-4-4-4-21-21-21-2122-1-122-1-122-1-10000400000000-2-2112-12-10000000000000000000000
χ534-44-4-2-222440-4-444-4-40000-2-22222-2-20000000000004i−4i−4i4i000002i−2i−2i2i000000000000000000000000000000
χ544-44-4-2-222440-4-444-4-40000-2-22222-2-2000000000000−4i4i4i−4i00000−2i2i2i−2i000000000000000000000000000000
χ554-4-444-4-441-201-2-12-12004i−4i1-2-121-2-123i−3i003i−3i003i−3i0000000000000003-300i−2i−i2i0000000000000000000000
χ564-4-444-4-441-201-2-12-12004i−4i1-2-121-2-12−3i3i00−3i3i00−3i3i000000000000000-3300i−2i−i2i0000000000000000000000
χ574-4-444-4-441-201-2-12-1200−4i4i1-2-121-2-123i−3i003i−3i003i−3i000000000000000-3300−i2ii−2i0000000000000000000000
χ584-4-444-4-441-201-2-12-1200−4i4i1-2-121-2-12−3i3i00−3i3i00−3i3i0000000000000003-300−i2ii−2i0000000000000000000000
χ594-4-444-4-44-210-212-12-1004i−4i-212-1-212-1003i−3i003i−3i003i−3i0000000000000003-3−2ii2i−i0000000000000000000000
χ604-4-444-4-44-210-212-12-1004i−4i-212-1-212-100−3i3i00−3i3i00−3i3i000000000000000-33−2ii2i−i0000000000000000000000
χ614-4-444-4-44-210-212-12-100−4i4i-212-1-212-1003i−3i003i−3i003i−3i000000000000000-332i−i−2ii0000000000000000000000
χ624-4-444-4-44-210-212-12-100−4i4i-212-1-212-100−3i3i00−3i3i00−3i3i0000000000000003-32i−i−2ii0000000000000000000000
χ634-4-44-222-244044-4-4-4-40000-2-222-2-22200000000000044-4-40000022-2-2000000000000000000000000000000
χ644-4-44-222-244044-4-4-4-40000-2-222-2-222000000000000-4-44400000-2-222000000000000000000000000000000
χ658888-4-4-4-42-482-42-42-4-4-400-12-12-12-1222-4-4-1-122-1-1220000000000000000000000000000000000000000000
χ668888-4-4-4-42-4-82-42-42-44400-12-12-12-12-2-24411-2-211-2-20000000000000000000000000000000000000000000
χ678888-4-4-4-4-428-42-42-42-4-4002-12-12-12-1-4-42222-1-122-1-10000000000000000000000000000000000000000000
χ688888-4-4-4-4-42-8-42-42-4244002-12-12-12-144-2-2-2-211-2-2110000000000000000000000000000000000000000000
χ6988-8-88-88-82-40-24-242-400002-42-4-24-240000000000000000000000000000000000000000000000000000000
χ7088-8-88-88-8-4204-24-2-420000-42-424-24-20000000000000000000000000000000000000000000000000000000
χ7188-8-8-44-442-40-24-242-443−4300-12-121-21-2000033−23−23−3−323230000000000000000000000000000000000000000000
χ7288-8-8-44-442-40-24-242-4−434300-12-121-21-20000−3−3232333−23−230000000000000000000000000000000000000000000
χ7388-8-8-44-44-4204-24-2-4243−43002-12-1-21-210000−23−23332323−3−30000000000000000000000000000000000000000000
χ7488-8-8-44-44-4204-24-2-42−4343002-12-1-21-2100002323−3−3−23−23330000000000000000000000000000000000000000000
χ758-88-888-8-82-40-242-4-2400002-4-24-242-40000000000000000000000000000000000000000000000000000000
χ768-88-888-8-8-4204-2-424-20000-424-24-2-420000000000000000000000000000000000000000000000000000000
χ778-88-8-4-4442-40-242-4-240000-121-21-2-120000−3i33i3003i3−3i3000000000000000000000000000000000000000000000
χ788-88-8-4-4442-40-242-4-240000-121-21-2-1200003i3−3i300−3i33i3000000000000000000000000000000000000000000000
χ798-88-8-4-444-4204-2-424-200002-1-21-212-1000000−3i33i3003i3−3i30000000000000000000000000000000000000000000
χ808-88-8-4-444-4204-2-424-200002-1-21-212-10000003i3−3i300−3i33i30000000000000000000000000000000000000000000
χ818-8-88-444-42-402-4-24-240000-121-2-121-26i−6i00−3i3i00−3i3i000000000000000000000000000000000000000000000
χ828-8-88-444-42-402-4-24-240000-121-2-121-2−6i6i003i−3i003i−3i000000000000000000000000000000000000000000000
χ838-8-88-444-4-420-424-24-200002-1-212-1-21006i−6i00−3i3i00−3i3i0000000000000000000000000000000000000000000
χ848-8-88-444-4-420-424-24-200002-1-212-1-2100−6i6i003i−3i003i−3i0000000000000000000000000000000000000000000

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