Finite Group Databasebeta

← Group #13167505

Character table — Group #13167505

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222244444444444444888888888888888888181818181818363636363636363636363636363636363636363636363636363636727272727272
order122234466633666666121212121212336666661212121212121212121244121212122224466666688881212121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-2-2-2-20000-2-200000000000000000000000000
χ1022222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2200002200000000000000000000000000
χ112222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-120000-1-1000022220000-1-1-1-1-1-1-1-1000000
χ122222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-120000-1-10000-2-2-2-2000011111111000000
χ132222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-200001100000000000033−3−333−3−3000000
χ142222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2000011000000000000−3−333−3−333000000
χ152222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-2000011000022-2-20000-1-1-1-11111000000
χ162222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-20000110000-2-22200001111-1-1-1-1000000
χ172222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2111120000-1-100000000000033−3−3−3−333000000
χ182222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2111120000-1-1000000000000−3−33333−3−3000000
χ192-22-222i−2i2-2-222-22-22-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i000000000000000002−2−i2i200002−22−2−i2i2−i2i2000000
χ202-22-222i−2i2-2-222-22-22-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000−22i2−i20000−22−22i2−i2i2−i2000000
χ212-22-22−2i2i2-2-222-22-22-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i000000000000000002−2i2−i200002−22−2i2−i2i2−i2000000
χ222-22-22−2i2i2-2-222-22-22-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000−22−i2i20000−22−22−i2i2−i2i2000000
χ232-22-2-12i−2i-11122-22-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii0033−3−300000−i3i300002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ242-22-2-12i−2i-11122-22-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii0033−3−300000−i3i30000−22i2−i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ252-22-2-12i−2i-11122-22-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii00−3−33300000i3−i300002−2−i2i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ262-22-2-12i−2i-11122-22-22-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii00−3−33300000i3−i30000−22i2−i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ272-22-2-1−2i2i-11122-22-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i0033−3−300000i3−i300002−2i2−i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ282-22-2-1−2i2i-11122-22-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i0033−3−300000i3−i30000−22−i2i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ292-22-2-1−2i2i-11122-22-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i00−3−33300000−i3i300002−2i2−i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ302-22-2-1−2i2i-11122-22-22-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i00−3−33300000−i3i30000−22−i2i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ312-2-22200-2-2222-2-2-2-22200000022-2-2-2-22200000000002-22-22-20002-2000000000022-2-200000000000000
χ322-2-22200-2-2222-2-2-2-22200000022-2-2-2-22200000000002-22-22-2000-220000000000-2-22200000000000000
χ332-2-22200-2-2222-2-2-2-22200000022-2-2-2-2220000000000-22-22-2202-2000022-2-20000000000000000000000
χ342-2-22200-2-2222-2-2-2-22200000022-2-2-2-2220000000000-22-22-220-220000-2-2220000000000000000000000
χ3544444444441-21-2-211-244-2-2-2-21-21-21-21-21111-2-211-2-200000000000000000000000000000000022-1-1-1-1
χ3644444444441-21-2-211-244-2-2-2-21-21-21-21-21111-2-211-2-2000000000000000000000000000000000-2-21111
χ374444444444-21-211-2-21441111-21-21-21-21-2-2-2-211-2-2110000000222200-1-1-1-10000-1-1-1-100000000000000
χ384444444444-21-211-2-21441111-21-21-21-21-2-2-2-211-2-2110000000-2-2-2-20011110000111100000000000000
χ3944444-4-44441-21-2-211-2-4-422221-21-21-21-2-1-1-1-122-1-1220000000000000000000000000000000002-2-1-111
χ4044444-4-44441-21-2-211-2-4-422221-21-21-21-2-1-1-1-122-1-122000000000000000000000000000000000-2211-1-1
χ4144444-4-4444-21-211-2-21-4-4-1-1-1-1-21-21-21-212222-1-122-1-1000000022-2-200-1-1-1-10000111100000000000000
χ4244444-4-4444-21-211-2-21-4-4-1-1-1-1-21-21-21-212222-1-122-1-10000000-2-2220011110000-1-1-1-100000000000000
χ4344-4-4400-44-4444-44-4-4-400000044-4-444-4-40000000000000000000000000000000000000000000000000
χ4444-4-4400-44-4-21-2-1122-1003i−3i3i−3i-212-1-212-100003i−3i003i−3i0000000000000−i3i3−i3i300003−33−300000000000000
χ4544-4-4400-44-4-21-2-1122-1003i−3i3i−3i-212-1-212-100003i−3i003i−3i0000000000000i3−i3i3−i30000−33−3300000000000000
χ4644-4-4400-44-4-21-2-1122-100−3i3i−3i3i-212-1-212-10000−3i3i00−3i3i0000000000000−i3i3−i3i30000−33−3300000000000000
χ4744-4-4400-44-4-21-2-1122-100−3i3i−3i3i-212-1-212-10000−3i3i00−3i3i0000000000000i3−i3i3−i300003−33−300000000000000
χ4844-4-4-2002-22444-44-4-4-4000000-2-222-2-22200000000000023−23−2323000000000000000000000000000000000
χ4944-4-4-2002-22444-44-4-4-4000000-2-222-2-222000000000000−232323−23000000000000000000000000000000000
χ504-44-444i−4i4-4-41-2-1-221-124i−4i−2i−2i2i2i1-21-2-12-12i−iii−2i−2i−i−i2i2i00000000000000000000000000000000000−i3i33−3
χ514-44-444i−4i4-4-41-2-1-221-124i−4i−2i−2i2i2i1-21-2-12-12i−iii−2i−2i−i−i2i2i00000000000000000000000000000000000i3−i3−33
χ524-44-444i−4i4-4-4-2121-1-22-14i−4iii−i−i-21-212-12-1−2i2i−2i−2iii2i2i−i−i0000000000000−i3i3i3−i300003−3−3300000000000000
χ534-44-444i−4i4-4-4-2121-1-22-14i−4iii−i−i-21-212-12-1−2i2i−2i−2iii2i2i−i−i0000000000000i3−i3−i3i30000−333−300000000000000
χ544-44-44−4i4i4-4-41-2-1-221-12−4i4i2i2i−2i−2i1-21-2-12-12−ii−i−i2i2iii−2i−2i00000000000000000000000000000000000−i3i3−33
χ554-44-44−4i4i4-4-41-2-1-221-12−4i4i2i2i−2i−2i1-21-2-12-12−ii−i−i2i2iii−2i−2i00000000000000000000000000000000000i3−i33−3
χ564-44-44−4i4i4-4-4-2121-1-22-1−4i4i−i−iii-21-212-12-12i−2i2i2i−i−i−2i−2iii0000000000000−i3i3i3−i30000−333−300000000000000
χ574-44-44−4i4i4-4-4-2121-1-22-1−4i4i−i−iii-21-212-12-12i−2i2i2i−i−i−2i−2iii0000000000000i3−i3−i3i300003−3−3300000000000000
χ584-4-44400-4-44-212-1-12-21003-3-33-212-12-1-2100003-300-3300000002-22-200-1-1110000-1-11100000000000000
χ594-4-44400-4-44-212-1-12-21003-3-33-212-12-1-2100003-300-330000000-22-220011-1-1000011-1-100000000000000
χ604-4-44400-4-44-212-1-12-2100-333-3-212-12-1-210000-33003-300000002-2-2200-1-111000011-1-100000000000000
χ614-4-44400-4-44-212-1-12-2100-333-3-212-12-1-210000-33003-30000000-222-20011-1-10000-1-11100000000000000
χ624-4-44-20022-244-4-4-4-444000000-2-22222-2-200000000004-4-22-22000000000000000000000000000000000
χ634-4-44-20022-244-4-4-4-444000000-2-22222-2-20000000000-442-22-2000000000000000000000000000000000
χ648888-488-4-4-42-42-4-422-4-4-4-4-4-4-4-12-12-12-1222-1-122-1-122000000000000000000000000000000000000000
χ658888-488-4-4-4-42-422-4-42-4-422222-12-12-12-1-4-422-1-122-1-1000000000000000000000000000000000000000
χ668888-4-8-8-4-4-42-42-4-422-4444444-12-12-12-12-2-211-2-211-2-2000000000000000000000000000000000000000
χ678888-4-8-8-4-4-4-42-422-4-4244-2-2-2-22-12-12-12-144-2-211-2-211000000000000000000000000000000000000000
χ6888-8-8800-88-82-424-4-2-240000002-4-242-4-240000000000000000000000000000000000000000000000000
χ6988-8-8-4004-442-424-4-2-24000000-121-2-121-20033−330033−3300000000000000000000000000000000000000000
χ7088-8-8-4004-442-424-4-2-24000000-121-2-121-200−333300−333300000000000000000000000000000000000000000
χ7188-8-8-4004-44-42-4-2244-2006i−6i6i−6i2-1-212-1-210000−3i3i00−3i3i000000000000000000000000000000000000000
χ7288-8-8-4004-44-42-4-2244-200−6i6i−6i6i2-1-212-1-2100003i−3i003i−3i000000000000000000000000000000000000000
χ738-88-8-48i−8i-4442-4-2-442-24−4i4i−4i−4i4i4i-12-121-21-22i−2i−i−i2i2iii−2i−2i000000000000000000000000000000000000000
χ748-88-8-48i−8i-444-4242-2-44-2−4i4i2i2i−2i−2i2-12-1-21-21−4i4i2i2i−i−i−2i−2iii000000000000000000000000000000000000000
χ758-88-8-4−8i8i-4442-4-2-442-244i−4i4i4i−4i−4i-12-121-21-2−2i2iii−2i−2i−i−i2i2i000000000000000000000000000000000000000
χ768-88-8-4−8i8i-444-4242-2-44-24i−4i−2i−2i2i2i2-12-1-21-214i−4i−2i−2iii2i2i−i−i000000000000000000000000000000000000000
χ778-8-88800-8-882-4-244-22-40000002-4-24-242-40000000000000000000000000000000000000000000000000
χ788-8-88-40044-42-4-244-22-4000000-121-21-2-1200−3i33i3003i3−3i300000000000000000000000000000000000000000
χ798-8-88-40044-42-4-244-22-4000000-121-21-2-12003i3−3i300−3i33i300000000000000000000000000000000000000000
χ808-8-88-40044-4-424-2-24-42006-6-662-1-21-212-10000-33003-3000000000000000000000000000000000000000
χ818-8-88-40044-4-424-2-24-4200-666-62-1-21-212-100003-300-33000000000000000000000000000000000000000

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