Finite Group Databasebeta

← Group #13146693

Character table — Group #13146693

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222444121212121212121218181818181818182424242436363636363636363636363636363636363672727272727272727272
order12223666266336666664444121212126666224488881212242424242424242424666612121212
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111
χ511111111-1-1-111111111-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1
χ611111111-1-1-111111111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-111
χ711111111-1-1-111111111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111
χ811111111-1-1-111111111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111-1-1-11111-1-1
χ92222222222222222222-2-2-2-2-2-2-2-2222200000000-2-2000000000000000000
χ1022222222-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000022000000000000000000
χ1122-2-222-2-20002222-2-2-2-22i−2i000000000000002−2−i2i22i−2i22−2−2−i2−i2i2i20000000000
χ1222-2-222-2-20002222-2-2-2-22i−2i00000000000000−22i2−i22i−2i−2−222i2i2−i2−i20000000000
χ1322-2-222-2-20002222-2-2-2-2−2i2i000000000000002−2i2−i2−2i2i22−2−2i2i2−i2−i20000000000
χ1422-2-222-2-20002222-2-2-2-2−2i2i00000000000000−22−i2i2−2i2i−2−222−i2−i2i2i20000000000
χ152-2-222-2-2200022-2-22-22-2002-222-2-20000002-2000000000000000000002-200
χ162-2-222-2-2200022-2-22-22-2002-222-2-2000000-2200000000000000000000-2200
χ172-2-222-2-2200022-2-22-22-200-22-2-22200002-20000000000000000002-2000000
χ182-2-222-2-2200022-2-22-22-200-22-2-2220000-22000000000000000000-22000000
χ19444444444441-21-21-2-210000000011-2-20000000000000000002200-1-100-1-1
χ20444444444441-21-21-2-210000000011-2-2000000000000000000-2-200110011
χ2144444444444-21-21-211-200000000-2-21122220000000000000000-1-100-1-100
χ2244444444444-21-21-211-200000000-2-211-2-2-2-2000000000000000011001100
χ2344444444-4-4-41-21-21-2-2100000000-1-1220000000000000000002-200-1-10011
χ2444444444-4-4-41-21-21-2-2100000000-1-122000000000000000000-22001100-1-1
χ2544444444-4-4-4-21-21-211-20000000022-1-122-2-20000000000000000-1-1001100
χ2644444444-4-4-4-21-21-211-20000000022-1-1-2-22200000000000000001100-1-100
χ274-44-44-44-40001-2-12-1-221000000003-3000000000000000000000000−i3i300−i3i3
χ284-44-44-44-40001-2-12-1-221000000003-3000000000000000000000000i3−i300i3−i3
χ294-44-44-44-40001-2-12-1-22100000000-33000000000000000000000000−i3i300i3−i3
χ304-44-44-44-40001-2-12-1-22100000000-33000000000000000000000000i3−i300−i3i3
χ314-44-44-44-400044-4-4-44-440000000000000000000000000000000000000000
χ324-4-444-4-44000-212-1-2-11200000000003-32-22-20000000000000000-1100-1100
χ334-4-444-4-44000-212-1-2-11200000000003-3-22-2200000000000000001-1001-100
χ344-4-444-4-44000-212-1-2-1120000000000-332-2-220000000000000000-11001-100
χ354-4-444-4-44000-212-1-2-1120000000000-33-222-200000000000000001-100-1100
χ366666-3-3-3-36-3-3000000002222-1-1-1-1000000000000-1-13−33−33−33−30000000000
χ376666-3-3-3-36-3-3000000002222-1-1-1-1000000000000-1-1−33−33−33−330000000000
χ386666-3-3-3-36-3-300000000-2-2-2-2111100000000222211-1-1-1-1-1-1-1-10000000000
χ396666-3-3-3-36-3-300000000-2-2-2-2111100000000-2-2-2-211111111110000000000
χ406666-3-3-3-3-6330000000022-2-211110000000022-2-2-1-1-1-1-1-111110000000000
χ416666-3-3-3-3-6330000000022-2-2111100000000-2-222-1-11111-1-1-1-10000000000
χ426666-3-3-3-3-63300000000-2-222-1-1-1-1000000000000113−33−3−33−330000000000
χ436666-3-3-3-3-63300000000-2-222-1-1-1-100000000000011−33−333−33−30000000000
χ4466-6-6-3-3330−3i33i3000000002i−2i003−33−3000000002−2i2−i2−iiζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ4566-6-6-3-3330−3i33i3000000002i−2i003−33−300000000−22−i2i2−ii−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ4666-6-6-3-3330−3i33i300000000−2i2i00−33−33000000002−2−i2i2i−iζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ4766-6-6-3-3330−3i33i300000000−2i2i00−33−3300000000−22i2−i2i−i−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ4866-6-6-3-33303i3−3i3000000002i−2i00−33−33000000002−2i2−i2−iiζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ4966-6-6-3-33303i3−3i3000000002i−2i00−33−3300000000−22−i2i2−ii−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ5066-6-6-3-33303i3−3i300000000−2i2i003−33−3000000002−2−i2i2i−iζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ5166-6-6-3-33303i3−3i300000000−2i2i003−33−300000000−22i2−i2i−i−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ5288-8-888-8-80002-42-4-244-20000000000000000000000000000000000000000
χ5388-8-888-8-8000-42-424-2-240000000000000000000000000000000000000000
χ548-88-88-88-8000-424-242-2-40000000000000000000000000000000000000000
χ558-8-888-8-880002-4-2424-4-20000000000000000000000000000000000000000
χ5612-1212-12-66-6600000000000000023−23−232300000000000000000000000000000000
χ5712-1212-12-66-66000000000000000−232323−2300000000000000000000000000000000
χ5812-12-1212-666-600000000000004-4-2-22200000000000000000000000000000000
χ5912-12-1212-666-60000000000000-4422-2-200000000000000000000000000000000

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