Finite Group Databasebeta

← Group #10590868

Character table — Group #10590868

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222222244444444444444444444444444441818181818181818242424242424242424242424
order122233446666668888366612121212121212122424242424242424242424242424242444448888244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ511111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111
χ611111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ711111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1
χ811111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111-1-111
χ9222222-2-222222200002222-2-2-2-2-2-2-2-2000000000000000022-2-20000000000000000
χ10222222-2-222222200002222-2-2-2-2-2-2-2-20000000000000000-2-2220000000000000000
χ1122222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000002020-1-1-1-10000
χ1222222-1222-1-12-122222-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-20-2011110000
χ1322222-1222-1-12-12-2-2-2-2-1-1-1-1-12-1-1-12-1-1-2-2-2-21111111111110000000020-20-1-1110000
χ1422222-1222-1-12-12-2-2-2-2-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100000000-202011-1-10000
χ152222-1222-122-12-12222-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000002020000-1-1-1-1
χ162222-1222-122-12-12222-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000-20-200001111
χ172222-1222-122-12-1-2-2-2-2-1-1-1-12-1-1-12-1-1-11111-2-2-2-21111111100000000020-2000011-1-1
χ182222-1222-122-12-1-2-2-2-2-1-1-1-12-1-1-12-1-1-11111-2-2-2-211111111000000000-2020000-1-111
χ1922-2-2222-2-2-22-2-2200002-2-22-2-2-2-22222000000000000000000002i2i−2i−2i000000000000
χ2022-2-2222-2-2-22-2-2200002-2-22-2-2-2-2222200000000000000000000−2i−2i2i2i000000000000
χ2122-2-222-22-2-22-2-222i2i−2i−2i2-2-222222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000
χ2222-2-222-22-2-22-2-22−2i−2i2i2i2-2-222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ2322-2-22-1-22-21-1-2122i2i−2i−2i-111-1-12-1-11-2112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000−i3i33−30000
χ2422-2-22-1-22-21-1-2122i2i−2i−2i-111-1-12-1-11-2112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000i3−i3−330000
χ2522-2-22-1-22-21-1-212−2i−2i2i2i-111-1-12-1-11-211−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000−i3i3−330000
χ2622-2-22-1-22-21-1-212−2i−2i2i2i-111-1-12-1-11-211−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000i3−i33−30000
χ2722-2-2-12-221-221-2-12i2i−2i−2i-111-12-1-1-1-2111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000000000003−3−i3i3
χ2822-2-2-12-221-221-2-12i2i−2i−2i-111-12-1-1-1-2111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000000000000−33i3−i3
χ2922-2-2-12-221-221-2-1−2i−2i2i2i-111-12-1-1-1-2111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000000000003−3i3−i3
χ3022-2-2-12-221-221-2-1−2i−2i2i2i-111-12-1-1-1-2111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000000000000−33−i3i3
χ312-22-222002-2-2-22-22−22−222-2-2000000002−22−22−22−222−2−222−2−2002i−2i−i2i2−i2i2000000000000
χ322-22-222002-2-2-22-22−22−222-2-2000000002−22−22−22−222−2−222−2−200−2i2ii2−i2i2−i2000000000000
χ332-22-222002-2-2-22-2−22−2222-2-200000000−22−22−22−22−2−222−2−222002i−2ii2−i2i2−i2000000000000
χ342-22-222002-2-2-22-2−22−2222-2-200000000−22−22−22−22−2−222−2−22200−2i2i−i2i2−i2i2000000000000
χ352-2-222200-22-22-2-2−i2i2i2−i22-22-200000000−i2i2i2−i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22i−2i002−2−22000000000000
χ362-2-222200-22-22-2-2−i2i2i2−i22-22-200000000−i2i2i2−i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2−2i2i00−222−2000000000000
χ372-2-222200-22-22-2-2i2−i2−i2i22-22-200000000i2−i2−i2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22i−2i00−222−2000000000000
χ382-2-222200-22-22-2-2i2−i2−i2i22-22-200000000i2−i2−i2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2−2i2i002−2−22000000000000
χ3944444-2-4-44-2-24-240000-2-2-2-22-4222-422000000000000000000000000000000000000
χ404444-24-4-4-244-24-20000-2-2-2-2-4222-4222000000000000000000000000000000000000
χ414444-2-244-2-2-2-2-2-244441111-2-211-2-211-2-2-2-2-2-2-2-21111111100000000000000000000
χ424444-2-244-2-2-2-2-2-2-4-4-4-41111-2-211-2-21122222222-1-1-1-1-1-1-1-100000000000000000000
χ434444-2-2-4-4-2-2-2-2-2-20000111122-1-122-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000
χ444444-2-2-4-4-2-2-2-2-2-20000111122-1-122-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000
χ4544-4-44-24-4-42-2-4240000-222-22-422-24-2-2000000000000000000000000000000000000
χ4644-4-4-244-42-442-4-20000-222-2-42224-2-2-2000000000000000000000000000000000000
χ4744-4-4-2-24-422-222-200001-1-1122-1-1-2-211000000003-33-3-33-3300000000000000000000
χ4844-4-4-2-24-422-222-200001-1-1122-1-1-2-21100000000-33-333-33-300000000000000000000
χ4944-4-4-2-2-4422-222-24i4i−4i−4i1-1-11-2-21122-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i00000000000000000000
χ5044-4-4-2-2-4422-222-2−4i−4i4i4i1-1-11-2-21122-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii00000000000000000000
χ514-44-44-200422-4-2-422−2222−22-2-2220000000022−2222−22−22−22−2−222−2−22200000000000000000000
χ524-44-44-200422-4-2-4−2222−2222-2-22200000000−2222−22222−22−222−2−222−2−200000000000000000000
χ534-44-4-2400-2-4-424222−2222−22-2-22200000000−22−2222−2222−22−2−222−2−22200000000000000000000
χ544-44-4-2400-2-4-4242−2222−2222-2-222000000002−22−2−2222−222222−2−222−2−200000000000000000000
χ554-44-4-2-200-2222-2222−2222−2211-1-1003i−3i003i−3i−22−22−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000
χ564-44-4-2-200-2222-2222−2222−2211-1-100−3i3i00−3i3i−22−22−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000
χ574-44-4-2-200-2222-22−2222−222211-1-1003i−3i003i−3i2−22−22−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000
χ584-44-4-2-200-2222-22−2222−222211-1-100−3i3i00−3i3i2−22−22−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000
χ594-4-444-200-4-2242-4−2i22i22i2−2i2-22-2200000000−2i22i22i2−2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ604-4-444-200-4-2242-42i2−2i2−2i22i2-22-22000000002i2−2i2−2i22i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ614-4-44-240024-4-2-42−2i22i22i2−2i2-22-2200000000i2−i2−i2i2−2i22i22i2−2i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ624-4-44-240024-4-2-422i2−2i2−2i22i2-22-2200000000−i2i2i2−i22i2−2i2−2i22i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ634-4-44-2-2002-22-222−2i22i22i2−2i21-11-1003i−3i00−3i3ii2−i2−i2i2i2−i2−i2i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ2300000000000000000000
χ644-4-44-2-2002-22-222−2i22i22i2−2i21-11-100−3i3i003i−3ii2−i2−i2i2i2−i2−i2i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000000
χ654-4-44-2-2002-22-2222i2−2i2−2i22i21-11-1003i−3i00−3i3i−i2i2i2−i2−i2i2i2−i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ2300000000000000000000
χ664-4-44-2-2002-22-2222i2−2i2−2i22i21-11-100−3i3i003i−3i−i2i2i2−i2−i2i2i2−i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000

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