Finite Group Databasebeta

← Group #13146546

Character table — Group #13146546

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222444121212121212121218181818181818182424242436363636363636363636363636363636363672727272727272727272
order12223666412123366666622441212121212121212444466888824242424242424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ511111111-1-1-111111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ611111111-1-1-111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ711111111-1-1-111111111-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ811111111-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ92222222222222222222-2-2-2-2-2-2-2-222220000-2-20000000000000000000000
χ1022222222-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000220000000000000000000000
χ1122-2-22-2-2200022-2-222-2-2002-222-2-20000002i−2i00000000000000000000002i−2i
χ1222-2-22-2-2200022-2-222-2-2002-222-2-2000000−2i2i0000000000000000000000−2i2i
χ1322-2-22-2-2200022-2-222-2-200-22-2-22200002i−2i00000000000000000000002i−2i00
χ1422-2-22-2-2200022-2-222-2-200-22-2-2220000−2i2i0000000000000000000000−2i2i00
χ152-22-222-2-2000222-2-2-22-22-2000000000000002-2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i20000000000
χ162-22-222-2-2000222-2-2-22-22-2000000000000002-2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i20000000000
χ172-22-222-2-2000222-2-2-22-2-2200000000000000-22−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ182-22-222-2-2000222-2-2-22-2-2200000000000000-22i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ19444444444441-21-21-2-210000000011-2-2222200000000000000000000-1-1-1-1
χ20444444444441-21-21-2-210000000011-2-2-2-2-2-2000000000000000000001111
χ2144444444444-21-21-211-200000000-2-21100000000000000000022-1-1-1-10000
χ2244444444444-21-21-211-200000000-2-211000000000000000000-2-211110000
χ2344444444-4-4-41-21-21-2-2100000000-1-12222-2-200000000000000000000-1-111
χ2444444444-4-4-41-21-21-2-2100000000-1-122-2-2220000000000000000000011-1-1
χ2544444444-4-4-4-21-21-211-20000000022-1-10000000000000000002-2-1-1110000
χ2644444444-4-4-4-21-21-211-20000000022-1-1000000000000000000-2211-1-10000
χ2744-4-44-4-440001-2-121-22-1000000003-3002i−2i2i−2i00000000000000000000−ii−ii
χ2844-4-44-4-440001-2-121-22-1000000003-300−2i2i−2i2i00000000000000000000i−ii−i
χ2944-4-44-4-440001-2-121-22-100000000-33002i−2i−2i2i00000000000000000000−iii−i
χ3044-4-44-4-440001-2-121-22-100000000-3300−2i2i2i−2i00000000000000000000i−i−ii
χ314-4-444-44-400044-44-4-4-440000000000000000000000000000000000000000
χ324-4-444-44-4000-21212-1-1-200000000003i−3i00000000000000000000−i3i33−30000
χ334-4-444-44-4000-21212-1-1-200000000003i−3i00000000000000000000i3−i3−330000
χ344-4-444-44-4000-21212-1-1-20000000000−3i3i00000000000000000000−i3i3−330000
χ354-4-444-44-4000-21212-1-1-20000000000−3i3i00000000000000000000i3−i33−30000
χ366666-3-3-3-36-3-3000000002222-1-1-1-100000000-1-100003−33−33−33−30000000000
χ376666-3-3-3-36-3-3000000002222-1-1-1-100000000-1-10000−33−33−33−330000000000
χ386666-3-3-3-36-3-300000000-2-2-2-2111100000000112222-1-1-1-1-1-1-1-10000000000
χ396666-3-3-3-36-3-300000000-2-2-2-211110000000011-2-2-2-2111111110000000000
χ406666-3-3-3-3-6330000000022-2-2111100000000-1-122-2-2-1-1-1-111110000000000
χ416666-3-3-3-3-6330000000022-2-2111100000000-1-1-2-2221111-1-1-1-10000000000
χ426666-3-3-3-3-63300000000-2-222-1-1-1-1000000001100003−33−3−33−330000000000
χ436666-3-3-3-3-63300000000-2-222-1-1-1-100000000110000−33−333−33−30000000000
χ446-66-6-3-333033−33000000002-2003−33−300000000-11−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ456-66-6-3-333033−33000000002-2003−33−300000000-11i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ466-66-6-3-333033−3300000000-2200−33−33000000001-1−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ476-66-6-3-333033−3300000000-2200−33−33000000001-1i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ486-66-6-3-3330−3333000000002-200−33−3300000000-11−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ496-66-6-3-3330−3333000000002-200−33−3300000000-11i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ506-66-6-3-3330−333300000000-22003−33−3000000001-1−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ516-66-6-3-3330−333300000000-22003−33−3000000001-1i2−i2i2−i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ5288-8-88-8-88000-424-2-42-240000000000000000000000000000000000000000
χ538-88-888-8-80002-424-24-4-20000000000000000000000000000000000000000
χ548-88-888-8-8000-42-4-24-2240000000000000000000000000000000000000000
χ558-8-888-88-80002-4-2-4-24420000000000000000000000000000000000000000
χ561212-12-12-666-600000000000004-4-2-22200000000000000000000000000000000
χ571212-12-12-666-60000000000000-4422-2-200000000000000000000000000000000
χ5812-12-1212-66-6600000000000000023−23−232300000000000000000000000000000000
χ5912-12-1212-66-66000000000000000−232323−2300000000000000000000000000000000

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